Multiple solutions to a Dirichlet problem with p-Laplacian and nonlinearity depending on a parameter

Abstract

The homogeneous Dirichlet problem for an elliptic equation with p-Laplacian and concave-convex reaction term depending on a parameter is investigated. At least five nontrivial solutions for all sufficiently small are obtained via variational methods, truncation techniques and sub- and super-solution arguments. The special case is also examined.

Keywords

• concave-convex nonlinearities
• p-laplacian
• constant-sign solutions
• multiple solutions