Affiliation:
1. LMAP(UMR CNRS 5142) Bat. IPRA, Avenue de l’Université, F-64013Pau, France
2. Department of Mathematics, Indian Institute of Technology Delhi, Hauz Khaz,New Delhi-16, India
Abstract
AbstractIn this article, we study the following fractional elliptic equation with critical growth and singular nonlinearity:(-\Delta)^{s}u=u^{-q}+\lambda u^{{2^{*}_{s}}-1},\qquad u>0\quad\text{in }%
\Omega,\qquad u=0\quad\text{in }\mathbb{R}^{n}\setminus\Omega,where Ω is a bounded domain in {\mathbb{R}^{n}} with smooth boundary {\partial\Omega}, {n>2s}, {s\in(0,1)}, {\lambda>0}, {q>0} and {2^{*}_{s}=\frac{2n}{n-2s}}.
We use variational methods to show the existence and multiplicity of positive solutions with respect to the parameter λ.
Funder
Centre National de la Recherche Scientifique
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