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November/December 2012 Infinite semipositone problems with asymptotically linear growth forcing terms
D.D. Hai, Lakshmi Sankar, R. Shivaji
Differential Integral Equations 25(11/12): 1175-1188 (November/December 2012). DOI: 10.57262/die/1356012256


We study the existence of positive solutions to the singular problem \begin{equation*} \begin{cases} -\Delta_p u = \lambda f(u)-\frac{1}{u^{\alpha}} & \mbox{ in } \Omega, \\ u = 0 & \mbox{ on } \partial \Omega, \end{cases} \end{equation*} where $\lambda$ is a positive parameter, $\Delta_p u =\operatorname{div}(|\nabla{u}|^{p-2}\nabla{u})$, $p > 1$, $\Omega $ is a bounded domain in $\mathbb{R}^{n}, n \geq 1$ with smooth boundary $\partial\Omega$, $0 < \alpha < 1$, and $f:[0,\infty) \rightarrow \mathbb{R}$ is a continuous function which is asymptotically $p$-linear at $\infty$. We prove the existence of positive solutions for a certain range of $\lambda$ using the method of sub-supersolutions. We also extend our study to classes of systems which have forcing terms satisfying a combined asymptotically p-linear condition at $\infty$ and to corresponding problems on exterior domains.


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D.D. Hai. Lakshmi Sankar. R. Shivaji. "Infinite semipositone problems with asymptotically linear growth forcing terms." Differential Integral Equations 25 (11/12) 1175 - 1188, November/December 2012.


Published: November/December 2012
First available in Project Euclid: 20 December 2012

zbMATH: 1274.35089
MathSciNet: MR3013409
Digital Object Identifier: 10.57262/die/1356012256

Primary: 35J75 , 35J92

Rights: Copyright © 2012 Khayyam Publishing, Inc.


Vol.25 • No. 11/12 • November/December 2012
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