Existence Results for Quasilinear Elliptic Equations with Indefinite Weight

Mieko Tanaka

Abstract and Applied Analysis, 2012, vol. 2012, issue 1

Abstract: We provide the existence of a solution for quasilinear elliptic equation -div(a∞(x)|∇u|p-2∇u+ã(x,|∇u|)∇u)=λm(x)|u|p-2u+f(x,u)+h(x) in Ω under the Neumann boundary condition. Here, we consider the condition that ã(x,t)=o(tp-2) as t → +∞ and f(x, u) = o(|u|p−1) as |u | → ∞. As a special case, our result implies that the following p‐Laplace equation has at least one solution: −Δpu = λm(x) | u|p−2u + μ | u|r−2u + h(x) in Ω, ∂u/∂ν = 0 on ∂Ω for every 1

Date: 2012
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https://doi.org/10.1155/2012/568120

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:568120

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