Multiplicity results of fractional $p$-Laplace equations with sign-changing and singular nonlinearity

In this article, we study the following fractional $p$-Laplacian equation with singular nonlinearity \begin{equation*} (P_{\la}) \left{ \begin{array}{lr} - 2\int_{\mb R^n}\frac{|w(y)-w(x)|^{p-2}(w(y)-w(x))}{|x-y|^{n+ps}}dy = a(x) w^{-q}+ \la b(x) w^r; $\text{in}$; \Om \quad \quad w>0;$\text{in}$;\Om, \quad w = 0 ; \mbox{in}; \mb R^n \setminus\Om, \end{array} \quad \right. \end{equation*} where $\text{Om}$ is a bounded domain in $\text{mb}{R}^n$ with smooth boundary $\partial \Om$,$n> ps$,$s\in(0,1)$,$\la>0$,$0<q<1$,$q<p-1<r< p_{s}^-1$with$p_{s}^=\frac{np}{n-ps}$,$a: \Om\subset\mb R^n \ra \mb R$suchthat$0< a(x)\in L^{\frac{p^{}_{s}}{p^{}{s}-1+q}}(\Om)$,and$b:\Om\subset\mb R^n \ra \mb R$isasign-changingfunctionsuchthat$b(x)\in L^{\frac{p^{*}{s}}{p^{*}_{s}-1-r}}(\Om)$. Using variational methods, we show existence and multiplicity of positive solutions of $(P_{\text{la}})$ with respect to the parameter $\text{la}$.