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Existence results for a class of nonlocal problems involving p ( x )‐Laplacian
Author(s) -
Allaoui Mostafa,
El Amrouss Abdel Rachid,
Ourraoui Anass
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3524
Subject(s) - mathematics , sobolev space , class (philosophy) , dirichlet distribution , exponent , variable (mathematics) , mathematical analysis , boundary (topology) , pure mathematics , dirichlet problem , dirichlet boundary condition , type (biology) , laplace operator , boundary value problem , ecology , linguistics , philosophy , artificial intelligence , computer science , biology
This paper is concerned with the existence of solutions to a class of p ( x )‐Kirchhoff‐type equations with Dirichlet boundary data as follows:− M∫ Ω1 p ( x ) | ∇ u | p ( x ) dx div ( | ∇ u | p ( x ) − 2 ∇ u ) = f ( x , u ) in Ω ,u = 0 on ∂ Ω .By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish some conditions on the existence of solutions. Copyright © 2015 John Wiley & Sons, Ltd.