Existence of solutions for perturbed fourth order elliptic equations with variable exponents

Thanh Chung, Nguyen: Existence of solutions for perturbed fourth order elliptic equations with variable exponents.

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Abstract

Using variational methods, we study the existence and multiplicity of solutions for a class of fourth order elliptic equations of the form 2 p(x) u − M �R 1 p(x) |∇u| p(x) dx� ∆p(x)u = f(x, u) in Ω, u = ∆u = 0 on ∂Ω, where Ω ⊂ RN, N ≥ 3, is a smooth bounded domain, ∆ 2 p(x) u = ∆(|∆u| p(x)−2∆u) is the operator of fourth order called the p(x)-biharmonic operator, ∆p(x)u = div |∇u| p(x)−2∇u is the p(x)-Laplacian, p : Ω → R is a log-Hölder continuous function, M : [0, +∞) → R and f : Ω × R → R are two continuous functions satisfying some certain condition.

Item Type: Journal
Publication full: Electronic journal of qualitative theory of differential equations
Date: 2018
Number: 96
ISSN: 1417-3875
Page Range: pp. 1-19
DOI: https://doi.org/10.14232/ejqtde.2018.1.96
Uncontrolled Keywords: Differenciálegyenlet - elliptikus, Kirchhoff típusú problémák
Additional Information: Bibliogr.: p. 16-19. ; összefoglalás angol nyelven
Date Deposited: 2019. Jan. 25. 12:02
Last Modified: 2020. Jul. 29. 12:29
URI: http://acta.bibl.u-szeged.hu/id/eprint/56908

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