Comparison principle for elliptic equations with mixed singular nonlinearities

We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle -\Delta_p u= \frac{f}{u^\gamma} + g u^q & \mbox{in \(\Omega\),} \\ u = 0 & \mbox{on \(\partial\Omega\),} \end{cases} \end{equation*} wher...

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Bibliographic Details
Published in:arXiv.org 2019-12
Main Authors: Durastanti, Riccardo, Oliva, Francescantonio
Format: Article
Language:English
Subjects:
Boundary value problems
Elliptic functions
Online Access:Get full text
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Summary:We deal with existence and uniqueness of positive solutions of an elliptic boundary value problem modeled by \begin{equation*} \begin{cases} \displaystyle -\Delta_p u= \frac{f}{u^\gamma} + g u^q & \mbox{in \(\Omega\),} \\ u = 0 & \mbox{on \(\partial\Omega\),} \end{cases} \end{equation*} where \(\Omega\) is an open bounded subset of \(\mathbb{R}^N\), \(\Delta_p u:=\text{div}(|\nabla u|^{p-2}\nabla u)\) is the usual \(p\)-Laplacian operator, \(\gamma\geq 0\) and \(0\leq q\leq p-1\); \(f\) and \(g\) are nonnegative functions belonging to suitable Lebesgue spaces.
ISSN:2331-8422
DOI:10.48550/arxiv.1912.08261