Existence and multiplicity of solutions for quasilinear nonhomogeneous problems: An Orlicz-Sobolev space setting |
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Authors: | Mihai Mih?ilescu |
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Institution: | Department of Mathematics, University of Craiova, 200585 Craiova, Romania |
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Abstract: | We study the boundary value problem −div(log(1+q|∇u|)|∇u|p−2∇u)=f(u) in Ω, u=0 on ∂Ω, where Ω is a bounded domain in RN with smooth boundary. We distinguish the cases where either f(u)=−λ|u|p−2u+|u|r−2u or f(u)=λ|u|p−2u−|u|r−2u, with p, q>1, p+q<min{N,r}, and r<(Np−N+p)/(N−p). In the first case we show the existence of infinitely many weak solutions for any λ>0. In the second case we prove the existence of a nontrivial weak solution if λ is sufficiently large. Our approach relies on adequate variational methods in Orlicz-Sobolev spaces. |
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Keywords: | Nonhomogeneous operator Orlicz-Sobolev space Critical point Weak solution |
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