Differential and Integral Equations

Positive solutions for a class of infinite semipositone problems

Abstract

We analyze the positive solutions to the singular boundary value problem $-\Delta u = \lambda[ f(u)-1/u^{\alpha}]; x \in \Omega$ $u = 0; \, x \in \partial\Omega,$ where $f$ is a $C^2$ function in $(0,\infty)$, $f(0)\geq 0,f^{'}>0, \lim_{s\rightarrow\infty}\frac{f(s)}{s}=0, \lambda$ is a positive parameter, $\alpha \in (0,1)$ and $\Omega$ is a bounded region in $R^{n}, n \geq 1$ with $C^{2+\gamma}$ boundary for some $\gamma \in (0,1)$. In the case $n=1$ we use the quadrature method and for $n>1$ we use the method of sub-super solution to establish our results.

Article information

Source
Differential Integral Equations, Volume 20, Number 12 (2007), 1423-1433.

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356039073

Mathematical Reviews number (MathSciNet)
MR2377025

Zentralblatt MATH identifier
1212.35129

Subjects
Primary: 35J60: Nonlinear elliptic equations
Secondary: 35J25: Boundary value problems for second-order elliptic equations

Citation

Ramaswamy, Mythily; Shivaji, R.; Ye, Jinglong. Positive solutions for a class of infinite semipositone problems. Differential Integral Equations 20 (2007), no. 12, 1423--1433. https://projecteuclid.org/euclid.die/1356039073