DOI: 10.2478/mjpaa-2023-0021 ISSN: 2351-8227
Solvability of Parametric Elliptic Systems with Variable Exponents
Anass Ouannasser, Abderrahmane El Hachimi- Applied Mathematics
- Control and Optimization
- Numerical Analysis
- Analysis
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.