A nonhomogeneous Steklov problem with $(p,q)$-Laplace differential operator

Abdelmajid BOUKHSAS; Mustapha BOURZIK; Abdellah Zerouali; Belhadj Karim

doi:10.5269/bspm.81383

A nonhomogeneous Steklov problem with $(p,q)$-Laplace differential operator

Abdelmajid BOUKHSAS Moulay Ismail University of Meknes, Faculty of Sciences and Technics, Department of Mathematics, Errachidia, Morocco. https://orcid.org/0000-0002-9317-8232
Mustapha BOURZIK Faculty of Sciences and Technics, Department of Mathematics, Errachidia, Morocco.
Abdellah Zerouali Regional Centre of Trades Education and Training, Oujda, Morocco.
Belhadj Karim Higher School for Education and Training, department of mathematics, Oujda, Morocco.

Résumé

We consider a nonlinear Steklov problem driven by the $(p,q)$-Laplacian operator with a concave parametric term and an asymmetric perturbation. We prove a multiplicity theorem producing three non-trivial solutions all with sign information(two positive and one negative), when the parameter is sufficiently small. Under a oddness condition near the origin for the perturbation.