Existence of three periodic solutions for a quasilinear periodic boundary value problem

Abstract

In this paper, we prove the existence of at least three periodic solutions for the quasilinear periodic boundary value problem \begin{eqnarray} \left\{ \begin{array}{ll} -p(x')x''+\alpha(t)x=\lambda f(t,x) ~{\rm a.e.} ~t\in[0,1], \\ x(1) -x(0)= x'(1)-x'(0)=0 \end{array} \right. \end{eqnarray} under appropriate hypotheses via a three critical points theorem of B. Ricceri. In addition, we give an example to illustrate the validity of our result.

Keywords

• periodic solutions
• three solutions
• critical point
• periodic boundary problem