Thanh Chung, Nguyen: Existence of solutions for perturbed fourth order elliptic equations with variable exponents. (2018)

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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 logHölder 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:  14173875 
Page Range:  pp. 119 
DOI:  https://doi.org/10.14232/ejqtde.2018.1.96 
Uncontrolled Keywords:  Differenciálegyenlet  elliptikus, Kirchhoff típusú problémák 
Additional Information:  Bibliogr.: p. 1619. ; összefoglalás angol nyelven 
Date Deposited:  2019. Jan. 25. 12:02 
Last Modified:  2020. Jul. 29. 12:29 
URI:  http://acta.bibl.uszeged.hu/id/eprint/56908 
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