On the Existence of Nontrivial Solutions of Inequalities in Orlicz-Sobolev Spaces
This paper is about an alternate variational inequality formulation for the boundary value problem −div(a(|∇u|)∇u)+∂uG(x,u)∋0 in Ω,u=0 on ∂Ω, where the principal part may have non-polynomial or very slow growth. As a consequence of this formulation, we can apply abstract nonsmooth linking theorems to study the existence and multiplicity of nontrivial solutions to the above problem.
V. K. Le, "On the Existence of Nontrivial Solutions of Inequalities in Orlicz-Sobolev Spaces," Discrete and Continuous Dynamical Systems - Series S, American Institute of Mathematical Sciences (AIMS), Jan 2012.
The definitive version is available at https://doi.org/10.3934/dcdss.2012.5.809
Mathematics and Statistics
Keywords and Phrases
nonsmooth functional; Mountain Pass theorem; Palais-Smale condition; Orlicz-Sobolev space
Article - Journal
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