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2006 Multiple positive solutions for classes of elliptic systems with combined nonlinear effects
Jaffar Ali, Mythily Ramaswamy, R. Shivaji
Differential Integral Equations 19(6): 669-680 (2006).

Abstract

We study the existence of multiple positive solutions to systems of the form \begin{equation*} \begin{cases} \qquad-{\Delta} u ={\lambda} f(v), & \text{ in }{\Omega},\\ \qquad-{\Delta} v ={\lambda} g(u), & \text{ in }{\Omega},\\ \qquad\quad~~ u=0=v, & \text{ on }{\partial}{\Omega}. \end{cases} \end{equation*} Here ${\Delta}$ is the Laplacian operator, ${\lambda}$ is a positive parameter, ${\Omega}$ is a bounded domain in ${\mathbb{R}^N}$ with smooth boundary and $f, g$ belong to a class of positive functions that have a combined sublinear effect at $\infty$. Our results also easily extend to the corresponding p-Laplacian systems. We prove our results by the method of sub and super solutions.

Citation

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Jaffar Ali. Mythily Ramaswamy. R. Shivaji. "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects." Differential Integral Equations 19 (6) 669 - 680, 2006.

Information

Published: 2006
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35162
MathSciNet: MR2234718

Subjects:
Primary: 35J55
Secondary: 35J60

Rights: Copyright © 2006 Khayyam Publishing, Inc.

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Vol.19 • No. 6 • 2006
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