Regularity of the lower positive branch for singular elliptic bifurcation problems

We consider the problem $$\displaylines{ -\Delta u=au^{-\alpha}+f(\lambda,\cdot,u) \quad\text{in }\Omega,\cr u=0\quad \text{on }\partial\Omega, \cr u>0 \quad \text{in }\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^n$, $\lambda\geq 0$, $0\leq a\in L^{\infty}(\Omega) $, and $0

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Bibliographic Details
Published in:Electronic journal of differential equations 2019-04, Vol.2019 (49), p.1-32
Main Authors: Tomas Godoy, Alfredo Guerin
Format: Article
Language:English
Subjects:
bifurcation problems
implicit function theorem
positive solutions
Singular elliptic problems
sub and super solutions
Online Access:Get full text
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Summary:We consider the problem $$\displaylines{ -\Delta u=au^{-\alpha}+f(\lambda,\cdot,u) \quad\text{in }\Omega,\cr u=0\quad \text{on }\partial\Omega, \cr u>0 \quad \text{in }\Omega, }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^n$, $\lambda\geq 0$, $0\leq a\in L^{\infty}(\Omega) $, and $0
ISSN:1072-6691