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

Figueiredo Giovany M. and Vetro Calogero: The existence of solutions for the modified (p(x), q(x))-Kirchhoff equation. (2022)

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We consider the Dirichlet problem Kp p(x) u(x) − ∆ Kq q(x) u(x) = f(x, u(x), ∇u(x)) in Ω, u = 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.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2022
Number: 39
ISSN: 1417-3875
Number of Pages: 16
Language: English
Place of Publication: Szeged
Uncontrolled Keywords: Differenciálegyenlet, Kirchhoff egyenlet, Dirichlet probléma
Additional Information: Bibliogr.: p. 14-16. ; összefoglalás angol nyelven
Subjects: 01. Natural sciences
01. Natural sciences > 01.01. Mathematics
Date Deposited: 2022. Sep. 08. 15:51
Last Modified: 2022. Nov. 08. 08:30

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