Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent

• Autorzy: Jia-Feng Liao , Jiu Liu , Peng Zhang , Chun-Lei Tang
• Języki publikacji: EN

Abstrakty

EN

We study the following singular elliptic equation with critical exponent
⎧$-Δu = Q(x)u^{2*-1} + λu^{-γ}$ in Ω,
⎨u > 0 in Ω,
⎩u = 0 on ∂Ω,
where $Ω ⊂ ℝ^{N}$ (N≥3) is a smooth bounded domain, and λ > 0, γ ∈ (0,1) are real parameters. Under appropriate assumptions on Q, by the constrained minimizer and perturbation methods, we obtain two positive solutions for all λ > 0 small enough.

Kategorie tematyczne

• 35A15: Variational methods
• 35J15: Second-order elliptic equations
• 35B09: Positive solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2016
• Tom: 116
• Numer: 3
• Strony: 273-292

Daty

wydano

2016

Twórcy

autor

Jia-Feng Liao

• School of Mathematics and Statistics, Southwest University, 400715 Chongqing, People's Republic of China
• School of Mathematics, and Computational Science, Zunyi Normal College, 563002 Zunyi, Guizhou, People's Republic of China

autor

Jiu Liu

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

autor

Peng Zhang

• School of Mathematics, and Computational Science, Zunyi Normal College, 563002 Zunyi, Guizhou, 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/ap3606-10-2015