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Articles 1 - 30 of 152
Full-Text Articles in Physical Sciences and Mathematics
Current Trends In Random Walks On Random Lattices, Jewgeni H. Dshalalow
Current Trends In Random Walks On Random Lattices, Jewgeni H. Dshalalow
Mathematics and System Engineering Faculty Publications
In a classical random walk model, a walker moves through a deterministic d-dimensional integer lattice in one step at a time, without drifting in any direction. In a more advanced setting, a walker randomly moves over a randomly configured (non equidistant) lattice jumping a random number of steps. In some further variants, there is a limited access walker’s moves. That is, the walker’s movements are not available in real time. Instead, the observations are limited to some random epochs resulting in a delayed information about the real-time position of the walker, its escape time, and location outside a bounded subset …
On A Class Of Elliptic Free Boundary Problems With Multiple Solutions, Kanishka Perera
On A Class Of Elliptic Free Boundary Problems With Multiple Solutions, Kanishka Perera
Mathematics and System Engineering Faculty Publications
We prove that a certain class of elliptic free boundary problems, which includes the Prandtl-Batchelor problem from fluid dynamics as a special case, has two distinct nontrivial solutions for large values of a parameter. The first solution is a global minimizer of the energy. The energy functional is nondifferentiable, so standard variational arguments cannot be used directly to obtain a second nontrivial solution. We obtain our second solution as the limit of mountain pass points of a sequence of C1-functionals approximating the energy. We use careful estimates of the corresponding energy levels to show that this limit is neither trivial …
Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad
Some New Nonlinear Second-Order Boundary Value Problems On An Arbitrary Domain, Ahmed Alsaedi, Mona Alsulami, Ravi P. Agarwal, Bashir Ahmad
Mathematics and System Engineering Faculty Publications
In this paper, we develop the existence theory for nonlinear second-order ordinary differential equations equipped with new kinds of nonlocal non-separated type integral multi-point boundary conditions on an arbitrary domain. Existence results are proved with the aid of fixed point theorems due to Schaefer, Krasnoselskii, and Leray–Schauder, while the uniqueness of solutions for the given problem is established by means of contraction mapping principle. Examples are constructed for the illustration of the obtained results. Ulam-stability is also discussed for the given problem. A variant of the problem involving different boundary data is also discussed. Finally, we introduce an associated boundary …
Lyapunov Functions To Caputo Fractional Neural Networks With Time-Varying Delays, Ravi P. Agarwal, Snezhana G. Hristova, Donal O'Regan
Lyapunov Functions To Caputo Fractional Neural Networks With Time-Varying Delays, Ravi P. Agarwal, Snezhana G. Hristova, Donal O'Regan
Mathematics and System Engineering Faculty Publications
One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable). In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when …
Variational Methods And Critical Point Theory 2013, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera
Variational Methods And Critical Point Theory 2013, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera
Mathematics and System Engineering Faculty Publications
[No abstract provided]
On The Optimal Control Of The Free Boundary Problems For The Second Order Parabolic Equations. I. Well-Posedness And Convergence Of The Method Of Lines, Ugur G. Abdulla
On The Optimal Control Of The Free Boundary Problems For The Second Order Parabolic Equations. I. Well-Posedness And Convergence Of The Method Of Lines, Ugur G. Abdulla
Mathematics and System Engineering Faculty Publications
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fi xed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework, where boundary heat flux and free boundary are components of the control vector, and optimality criteria consists of the mini- mization of the sum of L2-norm declinations from the available measurement of the temperature flux on the fi xed boundary and available information on the phase transition temperature on the free boundary. This approach allows one to tackle situations when …
Variational Methods And Critical Point Theory, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera
Variational Methods And Critical Point Theory, Victoria Otero-Espinar, Juan J. Nieto, Donal O'Regan, Kanishka Perera
Mathematics and System Engineering Faculty Publications
[No abstract provided]
Fixed Point Theorems For Convex-Power Condensing Operators Relative To The Weak Topology And Applications To Volterra Integral Equations, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi
Fixed Point Theorems For Convex-Power Condensing Operators Relative To The Weak Topology And Applications To Volterra Integral Equations, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi
Mathematics and System Engineering Faculty Publications
In this paper we present new fixed point theorems for weakly sequentially continuous mappings which are convex-power condensing relative to a measure of weak noncompactness. Our fixed point results extend and improve several earlier works. As an application, we investigate the existence of weak solutions to a Volterra integral equation. 2012 Rocky Mountain Mathematics Consortium.
Mixed Monotone-Generalized Contractions In Partially Ordered Probabilistic Metric Spaces, Łjubomir B.Bomir Ćirić, Ravi P. Agarwal, Bessem Samet
Mixed Monotone-Generalized Contractions In Partially Ordered Probabilistic Metric Spaces, Łjubomir B.Bomir Ćirić, Ravi P. Agarwal, Bessem Samet
Mathematics and System Engineering Faculty Publications
In this article, a new concept of mixed monotone-generalized contraction in partially ordered probabilistic metric spaces is introduced, and some coupled coincidence and coupled fixed point theorems are proved. The theorems Presented are an extension of many existing results in the literature and include several recent developments. © 2011 Ćirićć et al; licensee Springer.
Systems Of General Nonlinear Set-Valued Mixed Variational Inequalities Problems In Hilbert Spaces, Ravi P. Agarwal, Yeolje Cho, Narin Petrot
Systems Of General Nonlinear Set-Valued Mixed Variational Inequalities Problems In Hilbert Spaces, Ravi P. Agarwal, Yeolje Cho, Narin Petrot
Mathematics and System Engineering Faculty Publications
In this paper, the existing theorems and methods for finding solutions of systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces are studied. To overcome the difficulties, due to the presence of a proper convex lower semi-continuous function, φ and a mapping g, which appeared in the considered problem, we have used some applications of the resolvent operator technique. We would like to point out that although many authors have proved results for finding solutions of the systems of nonlinear set-valued (mixed) variational inequalities problems, it is clear that it cannot be directly applied to the problems …
Nonlocal Conditions For Differential Inclusions In The Space Of Functions Of Bounded Variations, Ravi P. Agarwal, Abdelkader Boucherif
Nonlocal Conditions For Differential Inclusions In The Space Of Functions Of Bounded Variations, Ravi P. Agarwal, Abdelkader Boucherif
Mathematics and System Engineering Faculty Publications
We discuss the existence of solutions of an abstract differential inclusion, with a right-hand side of bounded variation and subject to a nonlocal initial condition of integral type.
Solvability Of A Quadratic Hammerstein Integral Equation In The Class Of Functions Having Limits At Infinity, Ravi P. Agarwal, Józef Banas̈, Kamil Banas̈, Donal O'Regan
Solvability Of A Quadratic Hammerstein Integral Equation In The Class Of Functions Having Limits At Infinity, Ravi P. Agarwal, Józef Banas̈, Kamil Banas̈, Donal O'Regan
Mathematics and System Engineering Faculty Publications
The goal of the paper is to prove that a quadratic Hammerstein integral equation has solutions in the class of real functions denned, bounded, continuous on the real half-axis and having limits at infinity. The main tools used in our investigations are the technique of measures of noncompactness and the Darbo fixed point theorem. We provide an example illustrating our theory. © 2011 Rocky Mountain Mathematics Consortium.
Editorial Announcement, Ravi P. Agarwal
Editorial Announcement, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
[No abstract available]
Impulsive Semilinear Neutral Functional Differential Inclusions With Multivalued Jumps, Nadjet Abada, Ravi P. Agarwal, Mouffak Benchohra, Hadda Hammouche
Impulsive Semilinear Neutral Functional Differential Inclusions With Multivalued Jumps, Nadjet Abada, Ravi P. Agarwal, Mouffak Benchohra, Hadda Hammouche
Mathematics and System Engineering Faculty Publications
In this paper we establish sufficient conditions for the existence of mild solutions and extremal mild solutions for some densely defined impulsive semilinear neutral functional differential inclusions in separable Banach spaces. We rely on a fixed point theorem for the sum of completely continuous and contraction operators.
On Random Topological Structures, Ravi P. Agarwal, Yeolje Cho, Reza Saadati
On Random Topological Structures, Ravi P. Agarwal, Yeolje Cho, Reza Saadati
Mathematics and System Engineering Faculty Publications
We present some topics about random spaces. The main purpose of this paper is to study topological structure of random normed spaces and random functional analysis. These subjects are important to the study of nonlinear analysis in random normed spaces.
On The Existence Of Equilibrium Points, Boundedness, Oscillating Behavior And Positivity Of A Sveirs Epidemic Model Under Constant And Impulsive Vaccination, Manuel De La Sen, Ravi P. Agarwal, Asier Ibeas, Santiago Alonso-Quesada
On The Existence Of Equilibrium Points, Boundedness, Oscillating Behavior And Positivity Of A Sveirs Epidemic Model Under Constant And Impulsive Vaccination, Manuel De La Sen, Ravi P. Agarwal, Asier Ibeas, Santiago Alonso-Quesada
Mathematics and System Engineering Faculty Publications
This paper discusses the disease-free and endemic equilibrium points of a SVEIRS propagation disease model which potentially involves a regular constant vaccination. The positivity of such a model is also discussed as well as the boundedness of the total and partial populations. The model takes also into consideration the natural population growing and the mortality associated to the disease as well as the lost of immunity of newborns. It is assumed that there are two finite delays affecting the susceptible, recovered, exposed, and infected population dynamics. Some extensions are given for the case when impulsive nonconstant vaccination is incorporated at, …
Degenerate Anisotropic Differential Operators And Applications, Veli B. Shakhmurov
Degenerate Anisotropic Differential Operators And Applications, Veli B. Shakhmurov
Mathematics and System Engineering Faculty Publications
The boundary value problems for degenerate anisotropic differential operator equations with variable coefficients are studied. Several conditions for the separability and Fredholmness in Banach-valued Lp spaces are given. Sharp estimates for resolvent, discreetness of spectrum, and completeness of root elements of the corresponding differential operators are obtained. In the last section, some applications of the main results are given.
On A Generalized Time-Varying Seir Epidemic Model With Mixed Point And Distributed Time-Varying Delays And Combined Regular And Impulsive Vaccination Controls, Ravi P. Agarwal, Manuel De La Sen, Asier Ibeas, Santiago Alonso-Quesada
On A Generalized Time-Varying Seir Epidemic Model With Mixed Point And Distributed Time-Varying Delays And Combined Regular And Impulsive Vaccination Controls, Ravi P. Agarwal, Manuel De La Sen, Asier Ibeas, Santiago Alonso-Quesada
Mathematics and System Engineering Faculty Publications
This paper discusses a generalized time-varying SEIR propagation disease model subject to delays which potentially involves mixed regular and impulsive vaccination rules. The model takes also into account the natural population growing and the mortality associated to the disease, and the potential presence of disease endemic thresholds for both the infected and infectious population dynamics as well as the lost of immunity of newborns. The presence of outsider infectious is also considered. It is assumed that there is a finite number of time-varying distributed delays in the susceptible-infected coupling dynamics influencing the susceptible and infected differential equations. It is also …
Some Results For Integral Inclusions Of Volterra Type In Banach Spaces, Ravi P. Agarwal, Mouffak Benchohra, Juan Jose Nieto, Abdelghani Ouahab
Some Results For Integral Inclusions Of Volterra Type In Banach Spaces, Ravi P. Agarwal, Mouffak Benchohra, Juan Jose Nieto, Abdelghani Ouahab
Mathematics and System Engineering Faculty Publications
We first present several existence results and compactness of solutions set for the following Volterra type integral inclusions of the form: y(t) ∈ ∫0 t a(t-s)[Ay(s)+F(s,y(s)) ]ds,a.e.t ∈ J, where J=[ 0,b ], A is the infinitesimal generator of an integral resolvent family on a separable Banach space E, and F is a set-valued map. Then the Filippov's theorem and a Filippov-Waewski result are proved.
Positive Solutions Of Singular Complementary Lidstone Boundary Value Problems, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Positive Solutions Of Singular Complementary Lidstone Boundary Value Problems, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Mathematics and System Engineering Faculty Publications
We investigate the existence of positive solutions of singular problem (-1)mx(2m+1) = f(t, x,⋯, x(2m)), x (0) = 0, x(2i-1) (0) = x(2i-1) (T) = 0, 1 ≤ i ≤ m. Here, m ≥ 1 and the Carathéodory function f (t, x0,⋯, x2m) may be singular in all its space variables x0,⋯, x2m. The results are proved by regularization and sequential techniques. In limit processes, the Vitali convergence theorem is used.
Fixed Point Theorems For Ws-Compact Mappings In Banach Spaces, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi
Fixed Point Theorems For Ws-Compact Mappings In Banach Spaces, Ravi P. Agarwal, Donal O'Regan, Mohamed-Aziz Taoudi
Mathematics and System Engineering Faculty Publications
We present new fixed point theorems for ws-compact operators. Our fixed point results are obtained under Sadovskii, Leray-Schauder, Rothe, Altman, Petryshyn, and Furi-Pera type conditions. An example is given to show the usefulness and the applicability of our results.
Asymptotically Linear Solutions For Some Linear Fractional Differential Equations, Dumitru Baleanu, Octavian G. Mustafa, Ravi P. Agarwal
Asymptotically Linear Solutions For Some Linear Fractional Differential Equations, Dumitru Baleanu, Octavian G. Mustafa, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
We establish here that under some simple restrictions on the functional coefficient at the fractional differential equation 0Dα t tx − x x0 at x 0,t> 0, has a solution expressible as ct d o1 for t → ∞, where 0Dα t designates the Riemann-Liouville derivative of order α ∈ 0, 1 and c, d ∈ R.
Browder-Krasnoselskii-Type Fixed Point Theorems In Banach Spaces, Ravi P. Agarwal, Donal O'Regan
Browder-Krasnoselskii-Type Fixed Point Theorems In Banach Spaces, Ravi P. Agarwal, Donal O'Regan
Mathematics and System Engineering Faculty Publications
We present some fixed point theorems for the sum A+B of a weakly-strongly continuous map and a nonexpansive map on a Banach space X. Our results cover several earlier works by Edmunds, Reinermann, Singh, and others.
On Sumudu Transform And System Of Differential Equations, Adem Kiliçman, Hassan Eltayeb, Ravi P. Agarwal
On Sumudu Transform And System Of Differential Equations, Adem Kiliçman, Hassan Eltayeb, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
The regular system of differential equations with convolution terms solved by Sumudu transform.
On Type Of Periodicity And Ergodicity To A Class Of Fractional Order Differential Equations, Ravi P. Agarwal, Bruno D. Andrade, Claudio Cuevas
On Type Of Periodicity And Ergodicity To A Class Of Fractional Order Differential Equations, Ravi P. Agarwal, Bruno D. Andrade, Claudio Cuevas
Mathematics and System Engineering Faculty Publications
We study several types of periodicity to a class of fractional order differential equations.
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings, Ravi P. Agarwal, Xiaolong Qin, Shinmin Kang
On The Convergence Of An Implicit Iterative Process For Generalized Asymptotically Quasi-Nonexpansive Mappings, Ravi P. Agarwal, Xiaolong Qin, Shinmin Kang
Mathematics and System Engineering Faculty Publications
The purpose of this paper is to introduce and consider a general implicit iterative process which includes Schu's explicit iterative processes and Sun's implicit iterative processes as special cases for a finite family of generalized asymptotically quasi-nonexpansive mappings. Strong convergence of the purposed iterative process is obtained in the framework of real Banach spaces.
Impulsive Discontinuous Hyperbolic Partial Differential Equations Of Fractional Order On Banach Algebras, Said Abbas, Ravi P. Agarwal, Mouffak Benchohra
Impulsive Discontinuous Hyperbolic Partial Differential Equations Of Fractional Order On Banach Algebras, Said Abbas, Ravi P. Agarwal, Mouffak Benchohra
Mathematics and System Engineering Faculty Publications
This article studies the existence of solutions and extremal solutions to partial hyperbolic differential equations of fractional order with impulses in Banach algebras under Lipschitz and Carathéodory conditions and certain monotonicity conditions.
Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms, Ravi P. Agarwal, Shusen Ding
Global Caccioppoli-Type And Poincar ´E Inequalities With Orlicz Norms, Ravi P. Agarwal, Shusen Ding
Mathematics and System Engineering Faculty Publications
We obtain global weighted Caccioppoli-type and Poincaré inequalities in terms of Orlicz norms for solutions to the nonhomogeneous A -harmonic equation d A(x,d)=B(x,d).
Multiplicity Results For P-Sublinear P-Laplacian Problems Involving Indefinite Eigenvalue Problems Via Morse Theory, Kanishka Perera, Ravi P. Agarwal, Donal O'Regan
Multiplicity Results For P-Sublinear P-Laplacian Problems Involving Indefinite Eigenvalue Problems Via Morse Theory, Kanishka Perera, Ravi P. Agarwal, Donal O'Regan
Mathematics and System Engineering Faculty Publications
We establish some multiplicity results for a class of p-sublinear p- Laplacian problems involving indefinite eigenvalue problems using Morse theory.
Solutions Of A System Of Integral Equations In Orlicz Spaces, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong
Solutions Of A System Of Integral Equations In Orlicz Spaces, Ravi P. Agarwal, Donal O'Regan, Patricia J.Y. Wong
Mathematics and System Engineering Faculty Publications
We consider the following system of integral equations Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. Our aim is to establish criteria such that the above system has a solution (u±,U2,... ,un) where uiLφ (Orlicz space), 1 < i < n. We further investigate the system Ui(t) = ∫1gi(t,s)fi(s,u1(s),u2(s),...,un(s))ds, a.e. t [0,1], 1 ≤ i ≤ n. and establish the existence of constant-sign solutions in Orlicz spaces, i.e., for each 1 ≤ i ≤ n, Oui > 0 and ui G L