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

Abdelmajid Boukhsas; Abdellah Zerouali; Omar Chakrone; Academic Editor: Youssef EL FOUTAYENI

Research Communication | Open Access
Volume 2019 | Communication ID 129

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

Abdelmajid Boukhsas, Abdellah Zerouali, Omar Chakrone, Belhaj Karim

Academic Editor: Youssef EL FOUTAYENI

Received	Accepted	Published
Jan 28, 2019	Feb 26, 2019	Mar 01, 2019

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. $x\in\partial\Omega$.