Steklov spectrum and nonresonance for elliptic equations with nonlinear boundary conditions

Abstract

This article is devoted to the solvability of second order elliptic partial differential equations with nonlinear boundary conditions. We prove existence results when the nonlinearity on the boundary interacts, in some sense, with the Steklov spectrum. We obtain nonresonance results below the first Steklov eigenvalue as well as between two consecutive Steklov eigenvalues. Our method of proof is variational and relies mainly on minimax methods in critical point theory.

Keywords

• Steklov eigenvalues
• elliptic equations
• nonlinear boundary conditions
• minimax methods