Solvability of Parametric Elliptic Systems with Variable Exponents

Ouannasser, Anass; El Hachimi, Abderrahmane

doi:10.2478/mjpaa-2023-0021

Abstract

In this paper, we study the solvability to the left of the positive infimum of all eigenvalues for some non-resonant quasilinear elliptic problems involving variable exponents. We first prove the existence of at least a weak solution for some non-variational systems by using a surjectivity result for pseudomonotone operators. Furthermore, under additional conditions, we show that the solution is unique and provide examples. Second, we deal with non-resonant gradient-type systems and obtain existence by using a variational approach.

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Solvability of Parametric Elliptic Systems with Variable Exponents

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