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Full-Text Articles in Physical Sciences and Mathematics
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.