Article ID Journal Published Year Pages File Type
4616266 Journal of Mathematical Analysis and Applications 2014 17 Pages PDF
Abstract

In this paper, the existence and multiplicity results of solutions for the following quasilinear elliptic problemequation(0.1){−div(|x|−ap|∇u|p−2∇u)+h(x)|u|p−2u=g(x)|u|r−2u,x∈Ω,|x|−ap|∇u|p−2∂u∂ν=λf(x)|u|q−2u,x∈∂Ω are established, where Ω   is an exterior domain in RNRN with the compact and smooth boundary ∂Ω. By the variational methods, we prove that the problem (0.1) has at least two positive solutions. At the last part of the paper, we also consider the critical case and prove the existence of solution by concentration-compactness principle.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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