Study of some elliptic system of (p(x),q(x))-Kirchhoff type with convection

Springer Science and Business Media LLC - Tập 9 - Trang 687-704 - 2023
Noureddine Moujane1, Mohamed El Ouaarabi1, Chakir Allalou1
1Laboratory LMACS, Faculty of Science and Technology of Beni Mellal, Sultan Moulay Slimane University, Beni Mellal, Morocco

Tóm tắt

In this paper, we study the existence of weak solutions for a nonlocal elliptic system involving the (p(x), q(x))-Kirchhoff–Laplacian operators with Dirichlet boundary conditions, in the case of a reaction term depending also on the gradient (convection). Using a topological degree for a class of demicontinuous operators of generalized $$(S_+)$$ type, we obtain the existence result of weak solutions of the considered problem in the framework of Sobolev space with variable exponent. Our results extend and generalize some recent works in the existing literature.

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