Multiple solutions for a quasilinear second order differential equation depending on a parameter

Abstract

The purpose of this paper is to use a very recent three critical points theorem due to Bonanno and Marano to establish the existence of at least three solutions for the quasilinear second order differential equation on a compact interval [a, b] ⊂ R $$\left( {\begin{array}{*{20}{c}}{t - 1} \\3 \end{array}} \right) {u\left( a \right)}$$ under appropriate hypotheses. We exhibit the existence of at least three (weak) solutions and, and the results are illustrated by examples.