Multiple solutions to a perturbed Neumann problem

• Autorzy: Giuseppe Cordaro
• Języki publikacji: EN

Abstrakty

EN

We consider the perturbed Neumann problem
⎧ -Δu + α(x)u = α(x)f(u) + λg(x,u) a.e. in Ω,
⎨
⎩ ∂u/∂ν = 0 on ∂Ω,
where Ω is an open bounded set in $ℝ^{N}$ with boundary of class C², $α ∈ L^{∞}(Ω)$ with $ess inf_{Ω}α > 0$, f: ℝ → ℝ is a continuous function and g: Ω × ℝ → ℝ, besides being a Carathéodory function, is such that, for some p > N, $sup_{|s|≤t} |g(⋅,s)| ∈ L^{p}(Ω)$ and $g(⋅,t) ∈ L^{∞}(Ω)$ for all t ∈ ℝ. In this setting, supposing only that the set of global minima of the function $1/2 ξ² - ∫_{0}^{ξ} f(t)dt$ has M ≥ 2 bounded connected components, we prove that, for all λ ∈ ℝ small enough, the above Neumann problem has at least M+integer part of M/2 distinct strong solutions in $W^{2,p}(Ω)$.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2007
• Tom: 178
• Numer: 2
• Strony: 167-175

Daty

wydano

2007

Twórcy

autor

Giuseppe Cordaro

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

Identyfikatory

DOI

10.4064/sm178-2-3