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

Giovanni Anello; Giuseppe Cordaro

Colloquium Mathematicae (2003)

- Volume: 97, Issue: 2, page 221-231
- ISSN: 0010-1354

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topGiovanni Anello, and Giuseppe Cordaro. "Infinitely many positive solutions for the Neumann problem involving the p-Laplacian." Colloquium Mathematicae 97.2 (2003): 221-231. <http://eudml.org/doc/284810>.

@article{GiovanniAnello2003,

abstract = {We present two results on existence of infinitely many positive solutions to the Neumann problem
⎧ $-Δ_\{p\}u + λ(x)|u|^\{p-2\}u = μf(x,u)$ in Ω,
⎨
⎩ ∂u/∂ν = 0 on ∂Ω,
where $Ω ⊂ ℝ^\{N\}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ ∈ L^\{∞\}(Ω)$ with $essinf_\{x∈Ω\} λ(x) > 0$ 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.},

author = {Giovanni Anello, Giuseppe Cordaro},

journal = {Colloquium Mathematicae},

keywords = {-Laplacian; small solutions; positive solutions},

language = {eng},

number = {2},

pages = {221-231},

title = {Infinitely many positive solutions for the Neumann problem involving the p-Laplacian},

url = {http://eudml.org/doc/284810},

volume = {97},

year = {2003},

}

TY - JOUR

AU - Giovanni Anello

AU - Giuseppe Cordaro

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

JO - Colloquium Mathematicae

PY - 2003

VL - 97

IS - 2

SP - 221

EP - 231

AB - We present two results on existence of infinitely many positive solutions to the Neumann problem
⎧ $-Δ_{p}u + λ(x)|u|^{p-2}u = μf(x,u)$ in Ω,
⎨
⎩ ∂u/∂ν = 0 on ∂Ω,
where $Ω ⊂ ℝ^{N}$ is a bounded open set with sufficiently smooth boundary ∂Ω, ν is the outer unit normal vector to ∂Ω, p > 1, μ > 0, $λ ∈ L^{∞}(Ω)$ with $essinf_{x∈Ω} λ(x) > 0$ 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.

LA - eng

KW - -Laplacian; small solutions; positive solutions

UR - http://eudml.org/doc/284810

ER -

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