Electronic Journal of Differential Equations, 
Vol. 2021 (2021), No. 25, pp. 1-11.

Title: Existence and multiplicity of positive solutions for  singular p&q-Laplacian problems
       via sub-supersolution method
       
Authors: Suellen Cristina Q. Arruda (Univ. Federal do Para, Abaetetuba, PA, Brazil)
         Rubia G. Nascimento (Univ. Federal do Para, Belem, PA, Brazil)

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 
 $$\displaylines{
 -\text{div}(a(|\nabla u|^{p})|\nabla u|^{p-2}\nabla u)
 =h(x)u^{-\gamma}+  f(x,u) \quad \text{in } \Omega, \cr
 u>0\quad \text{in }\Omega, \cr
 u=0\quad\text{on } \partial\Omega,
 }$$
 where &Omega; is a bounded domain in R<sup>N</sup> with N&ge;3, 
 2&le;p&lt;N and &gamma;&gt;0. The hypotheses on the functions a, h,  
 and f allow us to extend this result to a large class of problems.

Submitted April 4, 2020. Published April 02, 2021.
Math Subject Classifications: 35B35, 35B40, 35K57, 35Q92, 92C17.
Key Words: p&amp;q-problem;  sub-supersolution method; singular elliptic problem.