Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 9 of 9
Full-Text Articles in Physical Sciences and Mathematics
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Lyapunov-Type Inequalities For $(\Mathtt{N},\Mathtt{P})$-Type Nonlinear Fractional Boundary Value Problems, Paul W. Eloe, Muralee Bala Krushna Boddu
Turkish Journal of Mathematics
This paper establishes Lyapunov-type inequalities for a family of two-point $(\mathtt{n},\mathtt{p})$-type boundary value problems for Riemann-Liouville fractional differential equations. To demonstrate how the findings can be applied, we provide a few examples, one of which is a fractional differential equation with delay.
Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki
Existence Of Fixed Points In Conical Shells Of A Banach Space For Sum Of Two Operators And Application In Odes, Amirouche Mouhous, Karima Mebarki
Turkish Journal of Mathematics
In this work a new functional expansion-compression fixed point theorem of Leggett--Williams type is developed for a class of mappings of the form $T+F,$ where $(I-T)$ is Lipschitz invertible map and $F$ is a $k$-set contraction. The arguments are based upon recent fixed point index theory in cones of Banach spaces for this class of mappings. As application, our approach is applied to prove the existence of nontrivial nonnegative solutions for three-point boundary value problem.
Existence Of Nonnegative Solutions For Discrete Robin Boundary Value Problems With Sign-Changing Weight, Yan Zhu
Turkish Journal of Mathematics
In this paper,~we are concerned with the following discrete problem first $$\left\{ \begin{array}{ll} -\Delta^{2}u(t-1)=\lambda p(t)f(u(t)), &t\in[1,N-1]_{\mathbb{Z}},\\ \Delta u(0)=u(N)=0,\\ \end{array} \right. $$ where $N>2$~is an integer,~$\lambda>0$~is a parameter,~$p:[1,N-1]_{\mathbb{Z}}\rightarrow\mathbb{R}$~is a sign-changing function,~$f:[0,+\infty)\rightarrow[0,+\infty)$~is a continuous and nondecreasing function.~$\Delta u(t)=u(t+1)-u(t)$,~$\Delta^{2}u(t)=\Delta(\Delta u(t))$.~By using the iterative method and Schauder's fixed point theorem,~we will show the existence of nonnegative solutions to the above problem. Furthermore, we obtain the existence of nonnegative solutions for discrete Robin systems with indefinite weights.
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Positive Periodic Solutions For A Class Of Second-Order Differential Equations With State-Dependent Delays, Ahleme Bouakkaz, Rabah Khemis
Turkish Journal of Mathematics
In this paper, we consider a class of second order differential equations with iterative source term. The main results are obtained by virtue of a Krasnoselskii fixed point theorem and some useful properties of a Green's function which allows us to prove the existence of positive periodic solutions. Finally, an example is included to illustrate the correctness of our results.
A Unique Solution To A Fourth-Order Three-Point Boundary Value Problem, Vedat Suat Ertürk
A Unique Solution To A Fourth-Order Three-Point Boundary Value Problem, Vedat Suat Ertürk
Turkish Journal of Mathematics
In this study, it is aimed to examine the solutions of the following nonlocal boundary value problem \begin{equation*} y^{(4)}+g(x,y)=0,x\in [{c,d}], y(c)=y'(c)=y''(c)=0,y(d)=\lambda y(\xi). \end{equation*} Here, $\xi\in ({c,d}),\lambda \in \mathbb{R},g\in C([{c,d}]\times \mathbb{R},\mathbb{R})$ and $g(x,0)\neq 0.$ It is concentrated on applications of Green's function that corresponds to the above problem to derive existence and uniqueness results for the solutions. One example is also given to demonstrate the results.
On The Solvability Of The Main Boundary Value Problems For A Nonlocal Poisson Equation, Valery Karachik, Abdizhahan Sarsenbi, Batirkhan Turmetov
On The Solvability Of The Main Boundary Value Problems For A Nonlocal Poisson Equation, Valery Karachik, Abdizhahan Sarsenbi, Batirkhan Turmetov
Turkish Journal of Mathematics
Solvability of the main boundary value problems for the nonlocal Poisson equation is studied. Existence and uniqueness theorems for the considered problems are obtained. The necessary and sufficient solvability conditions for all problems are given and integral representations for the solutions are constructed.
Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen
Lower And Upper Solutions Method For A Problem Of An Elastic Beam Whose One End Is Simply Supported And The Other End Is Sliding Clamped, Man Xu, Ruyun Ma, Jin Wen
Turkish Journal of Mathematics
In this paper we develop the lower and upper solutions method for the fourth-order boundary value problem of the form $$ \left\{ \aligned &y^{(4)}(x)+(k_{1}+k_{2})y''(x)+k_{1}k_{2}y(x)=f(x,y(x)), \ \ x\in (0,1),\\ &y(0)=y'(1)=y''(0)=y'''(1)=0,\\ \endaligned \right. $$ which models a statically elastic beam with one of its ends simply supported and the other end clamped by sliding clamps, where $k_{1}
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Sampling Theorem By Green's Function In A Space Ofvector-Functions, Hassan Atef Hassan
Turkish Journal of Mathematics
In this paper we give a sampling expansion for integral transforms whose kernels arise from Green's function of differential operators in a space of vector-functions. The differential operators are in a space of dimension $m$ and consist of systems of $m$ equations in $m$ unknowns. We assume the simplicity of the eigenvalues.
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
On Positive Solutions Of Boundary Value Problems For Nonlinear Second Order Difference Equations, Nüket Aykut, Gusein Sh. Guseinov
Turkish Journal of Mathematics
In this paper we study nonlinear second order difference equations subject to separated linear boundary conditions. Sign properties of the associated Green's functions are investigated and existence results for positive solutions of the nonlinear boundary value problem are established. Upper and lower bounds for these positive solutions also are given.