On singular nonpositone semilinear elliptic problems

Dinh Dang Hai

DOI: http://dx.doi.org/10.12775/TMNA.2008.034

Abstract


We prove the existence of a large positive solution for the boundary value
problems
$$
\alignat 2
-\Delta u &=\lambda (-h(u)+g(x,u))&\quad& \text{in }\Omega , \\
u &=0 &\quad &\text{on }\partial \Omega ,
\endalignat
$$
where $\Omega $ is a bounded domain in ${\mathbb R}^{N}$, $\lambda $ is
a positive parameter, $g(x,\cdot)$ is sublinear at $\infty$, and $h$ is
allowed to become $\infty $ at $u=0$. Uniqueness is also considered.

Keywords


Positive solutions; singular BVP; nonpositone

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