We consider the Dirichlet problem-Delta(Kp)(p(x))u(x) - Delta(Kq)(q(x))u(x) = f(x, u(x), del u(x)) in Omega, u vertical bar(partial derivative Omega) = 0,driven by the sum of a p(x)-Laplacian operator and of a q(x)-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and strong generalized solution, using topological tools (properties of Galerkin basis and of Nemitsky map). In the particular case of a positive Kirchhoff term, we obtain the existence of weak solution (= strong generalized solution), using the properties of pseudomonotone operators.

Figueiredo G.M., Vetro C. (2022). The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation. ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022(39), 1-16 [10.14232/ejqtde.2022.1.39].

The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation

Vetro C.
2022-08-27

Abstract

We consider the Dirichlet problem-Delta(Kp)(p(x))u(x) - Delta(Kq)(q(x))u(x) = f(x, u(x), del u(x)) in Omega, u vertical bar(partial derivative Omega) = 0,driven by the sum of a p(x)-Laplacian operator and of a q(x)-Laplacian operator, both of them weighted by indefinite (sign-changing) Kirchhoff type terms. We establish the existence of weak solution and strong generalized solution, using topological tools (properties of Galerkin basis and of Nemitsky map). In the particular case of a positive Kirchhoff term, we obtain the existence of weak solution (= strong generalized solution), using the properties of pseudomonotone operators.
27-ago-2022
Settore MAT/05 - Analisi Matematica
Figueiredo G.M., Vetro C. (2022). The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation. ELECTRONIC JOURNAL ON THE QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2022(39), 1-16 [10.14232/ejqtde.2022.1.39].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/571825
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