Opuscula Math. 45, no. 5 (2025), 665-684
https://doi.org/10.7494/OpMath.2025.45.5.665
Opuscula Mathematica
Systems of differential inclusions with competing operators and variable exponents
Francesca Vetro
Rakib Efendiev
Abstract. In this paper, we study a system of differential inclusions with Dirichlet boundary condition, involving competing operators and variable exponents. More precisely, we investigate the existence of both generalized solutions and weak solutions to the problem under consideration. In order to archive our results, we make use of approximation through finite dimensional subspaces via a Galerkin basis along with minimization and nonsmooth analysis.
Keywords: systems of differential inclusions, hemivariational inequalities, competing operators, Galerkin basis.
Mathematics Subject Classification: 49Q20, 49N60, 46E35.
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- Francesca Vetro (corresponding author)
https://orcid.org/0000-0001-7448-5299- Baku Engineering University, Scientific Research Center, Khirdalan City, Baku, Absheron, Azerbaijan
- Rakib Efendiev
- https://orcid.org/0000-0001-9864-5410
- Baku Engineering University, Department of Mathematics and Computer Science, Khirdalan City, Baku, Absheron, Azerbaijan
- Communicated by Vicenţiu D. Rădulescu.
- Received: 2025-05-16.
- Revised: 2025-08-11.
- Accepted: 2025-08-12.
- Published online: 2025-09-13.
