Multiplicity of Solutions for Quasilinear Elliptic Boundary-value Problems

Abstract

This paper is concerned with the existence of multiple solutions to the boundary-value problem -(ϕp(uf))f = λϕq (u)+ f (u) in (0, 1) , u(0) = u(1) = 0, where p, q > 1, ϕx(y) = |y|x−2y, λ is a real parameter, and f is a function which may be sublinear, superlinear, or asymmetric. We use the time map method for showing the existence of solutions.