THe Existence of two solutions for $(p(x),q(x))$-Laplacian problems with Steklov boundary conditions

Mostafa Rahmani; Belhadj Karim; Abdessamad Lakhdi; Abdellah  ZEROUALI

doi:10.5269/bspm.63157

Mostafa Rahmani
Belhadj Karim
Abdessamad Lakhdi https://orcid.org/0000-0002-0813-2898
Abdellah ZEROUALI

Abstract

The present paper discusses an elliptic equation with Steklov boundary conditions and $(p(x),q(x))$-Laplacian. Using mountain pass theorem together with Ekeland's variational principle, we prove, under appropriate conditions on the functions involved, that the problem admits at least two solutions.

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