Existence of solutions to superlinear p-Laplace equations without Ambrosetti-Rabinowizt condition
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Date
2017-10-10
Authors
Duc, Duong Minh
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
<p>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.