Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 155, pp. 1-6.
Title: Infinite semipositone problems with indefinite weight
and asymptotically linear growth forcing-terms
Authors: Ghasem A. Afrouzi (Univ. of Mazandaran, Babolsar, Iran)
Saleh Shakeri (Univ. of Mazandaran, Babolsar, Iran)
Abstract:
In this work, we study the existence of positive solutions to the
singular problem
$$\displaylines{
-\Delta_{p}u = \lambda m(x)f(u)-u^{-\alpha} \quad \hbox{in }\Omega,\cr
u = 0 \quad \hbox{on }\partial \Omega,
}$$
where $\lambda$ is positive parameter,
$\Omega $ is a bounded domain with smooth boundary,
$ 0 <\alpha<1 $, and $ f:[0,\infty] \to\mathbb{R}$ is a continuous
function which is asymptotically p-linear at $\infty $.
The weight function is continuous satisfies $m(x)>m_0>0$,
$\|m\|_{\infty}<\infty$. We prove the existence of a positive solution
for a certain range of $\lambda$ using the method of sub-supersolutions.
Submitted September 17, 2012. Published July 08, 2013.
Math Subject Classifications: 35J55, 35J25.
Key Words: Infinite semipositone problem; indefinite weight; forcing term;
asymptotically linear growth; sub-supersolution method.