Existence and multiplicity of solutions for a $p(x)$-Kirchhoff type problem via variational techniques
نویسندگان
چکیده
منابع مشابه
Existence and multiplicity of solutions for a class of fractional Kirchhoff-type problem∗
In this paper, we establish the existence and multiplicity of solutions to the following fractional Kirchhoff-type problem M(∥u∥)(−∆)u = f(x, u(x)), in Ω u = 0 in R\Ω, where N > 2s with s ∈ (0, 1), Ω is an open bounded subset of R with Lipschitz boundary, M and f are two continuous functions, and (−∆) is a fractional Laplace operator. Our main tools are based on critical point theorems and the ...
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* Correspondence: [email protected] Department of Mathematics, Northwest Normal University, Lanzhou 730070, P. R. China Abstract In this article, we study the existence and multiplicity of positive solutions for the Neumann boundary value problems involving the p(x)-Kirchhoff of the form ⎪⎨⎪⎩ −M (∫ 1 p(x) (|∇u|p(x) + λ|u|p(x))dx ) (div (|∇u|p(x)−2∇u) − λ|u|p(x)−2u) = f (x, u) in , ∂u ∂v = 0...
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Copyright q 2010 Bitao Cheng et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By using variational methods, we study the multiplicity of solutions for Kirchhoff type problems −a b Ω |∇u| 2 Δu f x, u, in Ω; u 0, on ∂Ω. Existe...
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In a previous paper [1], the author and Shmel’tser started the construction of an extended Lyusternik–Shnirelman–Morse theory for the study of single-valued and multivalued functionals on the space Ω̂(M) of losed directed curves in a manifold M. The authors applied these methods to the classical problem (Kirchhoffs problem) about the free motion of a rigid body in an ideal incompressible liquid,...
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ژورنال
عنوان ژورنال: Archivum Mathematicum
سال: 2015
ISSN: 0044-8753,1212-5059
DOI: 10.5817/am2015-3-163