Nonlinear resonant problems with an indefinite potential and concave boundary condition

Abstract

We consider a nonlinear elliptic problem driven by the $p$-Laplacian plus and indefinite potential term. The reaction is $(p-1)$-linear and resonant and the boundary term is concave. The problem is nonparametric. Using variational tools, together with truncation and perturbation techniques and critical groups, we show that the problem has at least three nontrivial smooth solutions.

Keywords

• resonant reaction
• concave boundary term
• critical group
• nonlinear regularity
• multiple solutions