Nonlinear nonhomogeneous Neumann eigenvalue problems

Abstract

We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.

Keywords

• superlinear reaction
• concave terms
• maximum principle
• extremal constant sign solutions
• nodal solution
• critical groups