Multiple solutions for a (p, q)-Laplacian Steklov problem

Abstract

In this paper we study the existence of at least three nontrivial solutions for the nonlinear $(p,q)$-Laplacian problem, with nonlinear boundary conditions. We establish that there exist at least three  non-zero solutions, under assumptions on the asymptotic behavior of the quotients $f(x,s)/|s|^{p-2}s$ and $pF(x,s)/|s|^{p}$ which extends the classical results with Dirichlet boundary conditions that for a.e. $x\in\partial\Omega$.