On nonlocal p(x)-Laplacian Dirichlet problems☆
By Xianling Fan. 2010
125 citations recorded by the source corpus.
Abstract This paper deals with the nonlocal p ( x ) -Laplacian Dirichlet problems with non-variational form − A ( u ) Δ p ( x ) u ( x ) = B ( u ) f ( x , u ( x ) ) in Ω ; u ∣ ∂ Ω = 0 , and with variational form − a ( ∫ Ω | ∇ u | p ( x ) p ( x ) d x ) Δ p ( x ) u ( x ) = b ( ∫ Ω F ( x , u ) d x ) f ( x , u ( x ) ) in Ω ; u ∣ ∂ Ω = 0 , where F ( x , t ) = ∫ 0 t f ( x , s ) d s , and a is allowed to be singular at zero. Using ( S + ) mapping theory and the variational method, some results on existence and multiplicity for the problems are obtained under weaker hypotheses. Our results are also new even for the case when p ( x ) ≡ p is a constant.
Subfields: Applied Mathematics, Computational Theory and Mathematics
View Paper: https://www.semanticscholar.org/paper/98fab9693eb0c20ac9a163bf2a2e874760f69b36
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In Applied Mathematics
In Computational Theory and Mathematics
Citations in the corpus
- Multiplicity results for a class of $p(x)$-Kirchhoff type equations with combined nonlinearities (2012, background): “Motivated by the papers [7, 8] and the ideas introduced in [10], the goal of this paper is to study the multiplicity of weak solutions for problem (1.”
- Three solutions for a nonlocal Dirichlet boundary value problem involving the p(x)-Laplacian (2013, methodology): “In 34 , by using ( S + ) mapping theory and the Mountain-Pass geometry, Fan has discussed the nonlocal p ( x )-Laplacian Dirichlet problem with non-variational form and nonlocal p ( x )-Laplacian Dirichlet problem with variational form respectively, and has obtained the existence of solutions”