Constant sign and nodal solutions for superlinear (p, q)–equations with indefinite potential and a concave boundary term

Abstract

We consider a nonlinear elliptic equation driven by the (p, q)–Laplacian plus an indefinite potential. The reaction is (p − 1)–superlinear and the boundary term is parametric and concave. Using variational tools from the critical point theory together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter, the problem has at least five nontrivial smooth solutions, all with sign information and which are linearly ordered.

Keywords

• superlinear reaction
• ar–condition
• concave boundary term
• constant sign and nodal solutions
• critical groups
• nonlinear regularity theory
• indefinite potential
• 35j20
• 35j60