Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations


Authors

Xiujuan Wang - School of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. China Aixia Qian - School of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. China


Abstract

This paper focuses on the following elliptic equation \[ \left\{ \begin{aligned} -u''- p(x)u=f(x,u),\quad \text{a.e.}\quad x\in[0,l],\\ u(0)-u(l)=u'(0)-u'(l)=0, \end{aligned} \right. \] where the primitive function of \(f(x,u)\) is either superquadratic or asymptotically quadratic as \(|u|\rightarrow\infty\), or subquadratic as \(|u|\rightarrow0\). By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establish the existence and multiplicity results for the periodic solution and subharmonic solution.


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