Existence of solutions to superlinear p-Laplace equations without Ambrosetti-Rabinowizt condition

Date

2017-10-10

Authors

Duc, Duong Minh

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Publisher

Texas State University, Department of Mathematics

Abstract

We study the existence of non-trivial weak solutions in W1,p0(Ω) of the super-linear Dirichlet problem -div(|∇u|p-2∇u) = ƒ(x, u) in Ω, u = 0 on ∂Ω, where ƒ satisfies the condition |ƒ(x, t)| ≤ |⍵(x)t|r-1 + b(x) ∀(x, t) ∈ Ω x ℝ, where r ∈ (p, Np/N-p), b ∈ L r/r-1 (Ω) and |⍵|r-1 may be non-integrable on Ω.

Description

Keywords

Nemytskii operators, p-Laplacian, Multiplicity of solutions, Mountain-pass theorem

Citation

Duc, D. M. (2017). Existence of solutions to superlinear p-Laplace equations without Ambrosetti-Rabinowizt condition. <i>Electronic Journal of Differential Equations, 2017</i>(251), pp. 1-10.

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Attribution 4.0 International

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