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![https://www.impan.pl/download/pdf/sm178-2-3 [zdalny]](images/mime-icons/pdf.gif "sm178-2-3.pdf")
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Języki publikacji
Abstrakty
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 $W^{2,p}(Ω)$.
⎧ -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 $W^{2,p}(Ω)$.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
167-175
Opis fizyczny
Daty
wydano
2007
Twórcy
autor
- Department of Mathematics, University of Messina, 98166 Sant'Agata-Messina, Italy
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-sm178-2-3
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