Existence of a positive ground state solution for a Kirchhoff type problem involving a critical exponent

• Autorzy: Lan Zeng , Chun Lei Tang
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 35A15: Variational methods
• 35B09: Positive solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 117
• Numer: 2
• Strony: 163-179

Daty

wydano

2016

Twórcy

autor

Lan Zeng

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, People's Republic of China

autor

Chun Lei Tang

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, People's Republic of China

Identyfikatory

DOI

10.4064/ap3783-1-2016