Multiplicity results for nonhomogeneous elliptic equations with singular nonlinearities

<p style='text-indent:20px;'>This paper is concerned with the study of multiple positive solutions to following elliptic problem involving a nonhomogeneous operator nonstandard growth <inline-formula><tex-math id="M1">\begin{document}$ p $\end{document}</tex-math></inline-formula>-<inline-formula><tex-math id="M2">\begin{document}$ q $\end{document}</tex-math></inline-formula> type and singular nonlinearities</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \left\{ \begin{alignedat}{2} {} - \mathcal{L}_{p,q} u & = \lambda \frac{f(u)}{u^\gamma}, \ u>0 && \quad\mbox{ in } \, \Omega, \\ 0 on \partial\Omega, \end{alignedat} \right. $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>where id="M3">\begin{document}$ \Omega bounded domain id="M4">\begin{document}$ \mathbb{R}^N id="M5">\begin{document}$ C^2 boundary, id="M6">\begin{document}$ N \geq 1 $\end{document}</tex-math></inline-formula>, id="M7">\begin{document}$ >0 real parameter,</p><p id="FE2"> : {\rm{div}}(|\nabla u|^{p-2} \nabla + |\nabla u|^{q-2} u), style='text-indent:20px;'><inline-formula><tex-math id="M8">\begin{document}$ 1<p<q< \infty id="M9">\begin{document}$ \gamma \in (0,1) id="M10">\begin{document}$ f continuous nondecreasing map satisfying suitable conditions. By constructing two distinctive pairs strict sub super solution, using fixed point theorems by Amann [<xref ref-type="bibr" rid="b1">1</xref>], we prove existence three cone id="M11">\begin{document}$ C_\delta(\overline{\Omega}) certain range id="M12">\begin{document}$ $\end{document}</tex-math></inline-formula>.</p>