Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
Jia-Feng Liao, Jiu Liu, Peng Zhang, Chun-Lei Tang
Annales Polonici Mathematici 116 (2016), 273-292
MSC: Primary 35J15; Secondary 35A15, 35B09.
DOI: 10.4064/ap3606-10-2015
Opublikowany online: 16 March 2016
Streszczenie
We study the following singular elliptic equation with critical exponent
$$
\begin{cases}
-\varDelta u=Q(x)u^{2^{*}-1}+\lambda u^{-\gamma}&\text{in } \varOmega, \\
u \gt 0 &\text{in } \varOmega, \\
u=0 &\text{on } \partial\varOmega,
\end{cases}
$$
where $\varOmega\subset\mathbb{R}^{N}$
$(N\geq3)$ is a smooth bounded domain, and
$\lambda \gt 0$,
$\gamma\in(0,1)$ are real parameters. Under appropriate assumptions on $Q,$
by the constrained minimizer and perturbation methods, we obtain two positive solutions for all $\lambda \gt 0$ small enough.
Autorzy
- Jia-Feng LiaoSchool of Mathematics and Statistics
Southwest University
400715 Chongqing
People’s Republic of China
and
School of Mathematics
and Computational Science
Zunyi Normal College
563002 Zunyi, Guizhou
People’s Republic of China
e-mail
- Jiu LiuSchool of Mathematics and Statistics
Southwest University
400715 Chongqing
People’s Republic of China
e-mail
- Peng ZhangSchool of Mathematics
and Computational Science
Zunyi Normal College
563002 Zunyi, Guizhou
People’s Republic of China
e-mail
- Chun-Lei TangSchool of Mathematics and Statistics
Southwest University
400715 Chongqing
People’s Republic of China
e-mail