On Dirichlet problem for fractional $p$-Laplacian with singular nonlinearity

Abstract

In this article, we study the following fractional $p$-Laplacian equation with critical growth singular nonlinearity \begin{equation*} \quad (-\De_{p})^s u = \la u^{-q} + u^α, u>0 \; \text{in}\; \Om,\quad u = 0 \; \mbox{in}\; \mb R^n \setminus\Om. \end{equation*} where $\Om$ is a bounded domain in $\mb{R}^n$ with smooth boundary $\partial \Om$, $n > sp, s \in (0,1), \la >0, 0 < q \leq 1 $ and $\alpha \le p_s^{\ast }-1$. We use variational methods to show the existence and multiplicity of positive solutions of above problem with respect to parameter $\la$.

26 pages

References in corpus (2)

• Critical growth fractional elliptic problem with singular nonlinearities
• The Brezis-Nirenberg problem for the fractional $p$-Laplacian

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• Least energy sign-changing solution of fractional $p$-Laplacian problems involving singularities