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We consider the following Kirchhoff type problem involving a critical nonlinearity:
⎧ $-[a+b(∫_{Ω} |∇u|²dx)^{m}]Δu = f(x,u) + |u|^{2*-2}u$ in Ω,
⎨
⎩ u = 0 on ∂Ω,
where $Ω ⊂ ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.
⎧ $-[a+b(∫_{Ω} |∇u|²dx)^{m}]Δu = f(x,u) + |u|^{2*-2}u$ in Ω,
⎨
⎩ u = 0 on ∂Ω,
where $Ω ⊂ ℝ^{N}$ (N ≥ 3) is a smooth bounded domain with smooth boundary ∂Ω, a > 0, b ≥ 0, and 0 < m < 2/(N-2). Under appropriate assumptions on f, we show the existence of a positive ground state solution via the variational method.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
163-179
Opis fizyczny
Daty
wydano
2016
Twórcy
autor
- School of Mathematics and Statistics, Southwest University, 400715 Chongqing, People's Republic of China
autor
- School of Mathematics and Statistics, Southwest University, 400715 Chongqing, People's Republic of China
Bibliografia
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-ap3783-1-2016