Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent
Annales Polonici Mathematici, Tome 116 (2016) no. 3, pp. 273-292
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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.
Keywords:
study following singular elliptic equation critical exponent begin cases vardelta u * lambda gamma text varomega text varomega text partial varomega end cases where varomega subset mathbb geq smooth bounded domain lambda gamma real parameters under appropriate assumptions constrained minimizer perturbation methods obtain positive solutions lambda small enough
Affiliations des auteurs :
Jia-Feng Liao 1 ; Jiu Liu 2 ; Peng Zhang 3 ; Chun-Lei Tang 2
@article{10_4064_ap3606_10_2015,
author = {Jia-Feng Liao and Jiu Liu and Peng Zhang and Chun-Lei Tang},
title = {Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent},
journal = {Annales Polonici Mathematici},
pages = {273--292},
publisher = {mathdoc},
volume = {116},
number = {3},
year = {2016},
doi = {10.4064/ap3606-10-2015},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap3606-10-2015/}
}
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Jia-Feng Liao; Jiu Liu; Peng Zhang; Chun-Lei Tang. Existence of two positive solutions for a class of semilinear elliptic equations with singularity and critical exponent. Annales Polonici Mathematici, Tome 116 (2016) no. 3, pp. 273-292. doi: 10.4064/ap3606-10-2015
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