Article ID Journal Published Year Pages File Type
4610141 Journal of Differential Equations 2015 29 Pages PDF
Abstract

The aim of this paper is investigating the existence of weak solutions of the quasilinear elliptic model problem{−div(A(x,u)|∇u|p−2∇u)+1pAt(x,u)|∇u|p=f(x,u)in Ω,u=0on ∂Ω, where Ω⊂RNΩ⊂RN is a bounded domain, N≥2N≥2, p>1p>1, A   is a given function which admits partial derivative At(x,t)=∂A∂t(x,t) and f is asymptotically p-linear at infinity.Under suitable hypotheses both at the origin and at infinity, and if A(x,⋅)A(x,⋅) is even while f(x,⋅)f(x,⋅) is odd, by using variational tools, a cohomological index theory and a related pseudo-index argument, we prove a multiplicity result if p>Np>N in the non-resonant case.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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