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Full-Text Articles in Mathematics
Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Existence And Rapid Convergence Results For Nonlinear Caputo Nabla Fractional Difference Equations, Xiang Liu, Baoguo Jia, Lynn Erbe, Allan Peterson
Department of Mathematics: Faculty Publications
This paper is concerned with finding properties of solutions to initial value problems for nonlinear Caputo nabla fractional difference equations. We obtain existence and rapid convergence results for such equations by use of Schauder’s fixed point theorem and the generalized quasi-linearization method, respectively. A numerical example is given to illustrate one of our rapid convergence results.
Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng
Existence And Behavior Of Positive Solutions To Elliptic System With Hardy Potential, Lei Wei, Xiyou Cheng, Zhaosheng Feng
School of Mathematical and Statistical Sciences Faculty Publications and Presentations
In this article, we study a class of elliptic systems with Hardy potentials. We analyze the possible behavior of radial solutions to the system when p; t > 1, q; s > 0 and λ; μ > (N - 2)2=4, and obtain the existence of positive solutions to the system with the Dirichlet boundary condition under certain conditions. When λ; μ > 0, p; t > 1 and q; s > 0, we show that any radial positive solution is decreasing in r.
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Solitary Waves In A Discrete Nonlinear Dirac Equation, Jesús Cuevas–Maraver, Panayotis G. Kevrekidis, Avadh Saxena
Mathematics and Statistics Department Faculty Publication Series
In the present work, we introduce a discrete formulation of the nonlinear Dirac equation in the form of a discretization of the Gross–Neveu model. The motivation for this discrete model proposal is both computational (near the continuum limit) and theoretical (using the understanding of the anti-continuum limit of vanishing coupling). Numerous unexpected features are identified including a staggered solitary pattern emerging from a single site excitation, as well as two- and three-site excitations playing a role analogous to one- and two-site excitations, respectively, of the discrete nonlinear Schrödinger analogue of the model. Stability exchanges between the two- and three-site states …
Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson
Characterization Of Partial Derivatives With Respect To Boundary Conditions For Solutions Of Nonlocal Boundary Value Problems For Nth Order Differential Equations, Jeffrey W. Lyons, Johnny Henderson
Mathematics Faculty Articles
Under certain conditions, solutions of the nonlocal boundary value problem, y(n) = f(x, y, y', ... , y(n- 1)), y(xi) = Yi for 1 £ i £ n- 1, and y(xn) - Σmk=1 Υiy (ni) = y n, are differentiated with respect to boundary conditions, where a < X1 < X2 < · · · < Xn-1 < n1 < · · · < nm < Xn < b, r1, ... , rm, Y1, ... , Yn ∈ R .
Dead Cores Of Singular Dirichlet Boundary Value Problems With Φ-Laplacian, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Dead Cores Of Singular Dirichlet Boundary Value Problems With Φ-Laplacian, Ravi P. Agarwal, Donal O'Regan, Svatoslav Staněk
Mathematics and System Engineering Faculty Publications
The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet problem (ϕ(u′))′ = λf(t, u, u′), u(0) = u(T) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and may be singular at the value A of its first and at the value 0 of its second phase variable.
Singular Positone And Semipositone Boundary Value Problems Of Second Order Delay Differential Equations, Daqing Jiang, Xiaojie Xu, Donal O'Regan, Ravi P. Agarwal
Singular Positone And Semipositone Boundary Value Problems Of Second Order Delay Differential Equations, Daqing Jiang, Xiaojie Xu, Donal O'Regan, Ravi P. Agarwal
Mathematics and System Engineering Faculty Publications
In this paper we present some new existence results for singular positone and semipositone boundary value problems of second order delay differential equations. Throughout our nonlinearity may be singular in its dependent variable.
Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu
Existence And Comparison Results For Quasilinear Evolution Hemivariational Inequalities, Siegfried Carl, Vy Khoi Le, Dumitru Motreanu
Mathematics and Statistics Faculty Research & Creative Works
We generalize the sub-supersolution method known for weak solutions of single and multivalued nonlinear parabolic problems to quasilinear evolution hemivariational inequalities. To this end we first introduce our basic notion of sub- and supersolutions on the basis of which we then prove existence, comparison, compactness and extremality results for the hemivariational inequalities under considerations.
Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang
Long Time Behavior Of Solutions To The 3d Compressible Euler Equations With Damping, Thomas C. Sideris, Becca Thomases, Dehua Wang
Mathematics Sciences: Faculty Publications
The effect of damping on the large-time behavior of solutions to the Cauchy problem for the three-dimensional compressible Euler equations is studied. It is proved that damping prevents the development of singularities in small amplitude classical solutions, using an equivalent reformulation of the Cauchy problem to obtain effective energy estimates. The full solution relaxes in the maximum norm to the constant background state at a rate of t-3/2. While the fluid vorticity decays to zero exponentially fast in time, the full solution does not decay exponentially. Formation of singularities is also exhibited for large data.
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Positive Solutions To Semilinear Problems With Coefficient That Changes Sign, Nguyen Phuong Cac, Juan A. Gatica, Yi Li
Mathematics and Statistics Faculty Publications
No abstract provided.
Quasilinear Evolution Equations In Nonclassical Diffusion, Kenneth Kuttler, Elias Aifantis
Quasilinear Evolution Equations In Nonclassical Diffusion, Kenneth Kuttler, Elias Aifantis
Faculty Publications
After describing the motivation leading to some nonclassical diffusion equations, we formulate a general abstract nonlinear evolution equation and establish existence of solutions. Then we return to the original equation and discuss particular initial-boundary value problems.