# POSITIVE SOLUTIONS OF A FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH PARAMETER

TitlePOSITIVE SOLUTIONS OF A FOURTH-ORDER PERIODIC BOUNDARY VALUE PROBLEM WITH PARAMETER
Publication TypeJournal Article
Year of Publication2018
AuthorsWU YANG, SUN JIAN-PING, ZHAO YA-HONG
JournalDynamic Systems and Applications
Volume27
Issue33
Start Page637
Pagination16
Date Published07/2018
ISSNDynamic Systems and Applications
AMS Subject Classification34B15
Abstract

In this paper, we study the following periodic boundary value problem of fourth-order ordinary differential equation
\begin{equation*}
\left\{
\begin{aligned}
&u^{(4)}(t)+\alpha u^{\prime\prime}(t)-\rho^{4}u(t)+\lambda f(t,u(t))=0,~t\in{[0,2\pi]},\\
&u^{(i)}(0)=u^{(i)}(2\pi),~i=0,1,2,3,\\
\end{aligned}
\right.
\end{equation*}
where $\alpha$ and $\rho$ are constants satisfying $\rho\neq0$ and $4\alpha+16\rho^{4}<1$, and $\lambda>0$ is a parameter. By imposing some conditions on the nonlinear term $f$, we obtain the existence and multiplicity of positive solutions to the above problem for suitable $\lambda$. The main tool used is Guo-Krasnoselskii fixed point theorem.

DOI10.12732/dsa.v27i3.12
Refereed DesignationRefereed
Full Text

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