2007 Positive solutions for a class of infinite semipositone problems
Mythily Ramaswamy, R. Shivaji, Jinglong Ye
Differential Integral Equations 20(12): 1423-1433 (2007). DOI: 10.57262/die/1356039073

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.

Citation

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Mythily Ramaswamy. R. Shivaji. Jinglong Ye. "Positive solutions for a class of infinite semipositone problems." Differential Integral Equations 20 (12) 1423 - 1433, 2007. https://doi.org/10.57262/die/1356039073

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35129
MathSciNet: MR2377025
Digital Object Identifier: 10.57262/die/1356039073

Subjects:
Primary: 35J60
Secondary: 35J25

Rights: Copyright © 2007 Khayyam Publishing, Inc.

Vol.20 • No. 12 • 2007
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