Infinitely many positive solutions for the Neumann problem involving the p-Laplacian

Giovanni Anello; Giuseppe Cordaro

Colloquium Mathematicae, Tome 96 (2003), p. 221-231 / Harvested from The Polish Digital Mathematics Library

Résumé

We present two results on existence of infinitely many positive solutions to the Neumann problem ⎧ $- Δ_{p} u + λ (x) {| u |}^{p - 2} u = μ f (x, u)$ in Ω, ⎨ ⎩ ∂u/∂ν = 0 on ∂Ω, where $Ω \subset ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ \in L^{\infty} (Ω)$ with $e s s i n f_{x \in Ω} λ (x) > 0$ and f: Ω × ℝ → ℝ is a Carathéodory function. Our results ensure the existence of a sequence of nonzero and nonnegative weak solutions to the above problem.

Publié le : 2003-01-01

Zbl 1046.35030

EUDML-ID : urn:eudml:doc:284810

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     title = {Infinitely many positive solutions for the Neumann problem involving the p-Laplacian},
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     year = {2003},
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Giovanni Anello; Giuseppe Cordaro. Infinitely many positive solutions for the Neumann problem involving the p-Laplacian. Colloquium Mathematicae, Tome 96 (2003) pp. 221-231. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm97-2-8/