Critical point approaches to quasilinear second order differential equations depending on a parameter

Abstract

In this paper, we make application of some three-critical points results to establish the existence of at least three solutions for a boundary value problem for the quasilinear second order differential equation on a compact interval $[a,b]\subset\mathbb{R}$, $$ \begin{cases} -u''=(\lambda f(x,u)+g(x,u))h(x,u') &\text{in } (a,b),\\ u(a)=u(b)=0, \end{cases} $$ under appropriate hypotheses. We exhibit the existence of at least three (weak) solutions.