Geodesic
Positive solutions for elliptic equations with singular nonlinearity
Electronic Journal of Differential Equations, Tome 2005 (2005).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We study an elliptic boundary-value problem with singular nonlinearity via the method of monotone iteration scheme: $$\displaylines{ -\Delta u(x)=f(x,u(x)),\quad x \in \Omega,\cr u(x)=\phi(x),\quad x \in \partial \Omega , }$$ where $\Delta$ is the Laplacian operator, $\Omega$ is a bounded domain in $\mathbb{R}^{N}, N \geq 2, \phi \geq 0$ may take the value 0 on $\partial\Omega$, and $f(x,s)$ is possibly singular near $s=0$. We prove the existence and the uniqueness of positive solutions under a set of hypotheses that do not make neither monotonicity nor strict positivity assumption on $f(x,s)$ which improvements of some previous results.
Classification : 35J25, 35J60
Keywords: singular nonlineararity, elliptic equation, positive solution, monotonic iteration 
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     author = {Shi, Junping and Yao, Miaoxin},
     title = {Positive solutions for elliptic equations with singular nonlinearity},
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     volume = {2005},
     year = {2005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a178/}
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Shi, Junping; Yao, Miaoxin. Positive solutions for elliptic equations with singular nonlinearity. Electronic Journal of Differential Equations, Tome 2005 (2005). http://geodesic.mathdoc.fr/item/EJDE_2005__2005__a178/