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

• Autorzy: Giovanni Anello , Giuseppe Cordaro
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35J20: Variational methods for second-order elliptic equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 97
• Numer: 2
• Strony: 221-231

Daty

wydano

2003

Twórcy

autor

Giovanni Anello

• Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy

autor

Giuseppe Cordaro

• Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy

Identyfikatory

DOI

10.4064/cm97-2-8