p(x)-Laplacian-like Neumann problems in variable-exponent Sobolev spaces via topological degree methods
Filomat, Tome 36 (2022) no. 17, p. 5973
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In this paper, we investigate the existence of a ”weak solutions” for a Neumann problems of p(x)-Laplacian-like operators, originated from a capillary phenomena, of the following form −div ( |∇u|p(x)−2∇u + |∇u| 2p(x)−2∇u√ 1 + |∇u|2p(x) ) = λ f (x,u,∇u) in Ω, ( |∇u|p(x)−2∇u + |∇u|2p(x)−2∇u√ 1+|∇u|2p(x) ) ∂u ∂η = 0 on ∂Ω, in the setting of the variable-exponent Sobolev spaces W1,p(x)(Ω), where Ω is a smooth bounded domain in RN, p(x) ∈ C+(Ω) and λ is a real parameter. Based on the topological degree for a class of demicontinuous operators of generalized (S+) type and the theory of variable-exponent Sobolev spaces, we obtain a result on the existence of weak solutions to the considered problem.
Classification :
35J60, 35D30, 47H11, 46E35
Keywords: p(x)-Laplacian-like operators, variable-exponent Sobolev spaces, capillarity phenomena, topological degree methods
Keywords: p(x)-Laplacian-like operators, variable-exponent Sobolev spaces, capillarity phenomena, topological degree methods
Mohamed El Ouaarabi; Chakir Allalou; Said Melliani. p(x)-Laplacian-like Neumann problems in variable-exponent Sobolev spaces via topological degree methods. Filomat, Tome 36 (2022) no. 17, p. 5973 . doi: 10.2298/FIL2217973E
@article{10_2298_FIL2217973E,
author = {Mohamed El Ouaarabi and Chakir Allalou and Said Melliani},
title = {p(x)-Laplacian-like {Neumann} problems in variable-exponent {Sobolev} spaces via topological degree methods},
journal = {Filomat},
pages = {5973 },
year = {2022},
volume = {36},
number = {17},
doi = {10.2298/FIL2217973E},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2217973E/}
}
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%0 Journal Article %A Mohamed El Ouaarabi %A Chakir Allalou %A Said Melliani %T p(x)-Laplacian-like Neumann problems in variable-exponent Sobolev spaces via topological degree methods %J Filomat %D 2022 %P 5973 %V 36 %N 17 %U http://geodesic.mathdoc.fr/articles/10.2298/FIL2217973E/ %R 10.2298/FIL2217973E %G en %F 10_2298_FIL2217973E
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