Existence and multiplicity of positive solutions for singular p&q-Laplacian problems via sub-supersolution method

Abstract

In this work we show the existence and multiplicity of positive solutions for a singular elliptic problem which the operator is non-linear and non-homogenous. We use the sub-supersolution method to study the following class of \(p\&q\)-singular problems $$\displaylines{ -\hbox{div}(a(|\nabla u|^{p})|\nabla u|^{p-2}\nabla u) =h(x)u^{-\gamma}+ f(x,u) \quad \text{in } \Omega, \cr u>0\quad \hbox{in }\Omega, \cr u=0\quad\text{on } \partial\Omega, }$$ where \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) with \(N\geq 3\), \(2\leq p<N\) and \(\gamma>0\). The hypotheses on the functions \(a\), \(h\), and \(f\) allow us to extend this result to a large class of problems. For more information see https://ejde.math.txstate.edu/Volumes/2021/25/abstr.html