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An existence result on positive solutions for a class of semilinear elliptic systems

Published online by Cambridge University Press:  12 July 2007

D. D. Hai  and
R. Shivaji
D. D. Hai
Affiliation:
Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA (dang@math.msstate.edu)
R. Shivaji
Affiliation:
Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA (shivaji@msstate.edu)
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Abstract

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Consider the system where λ is a positive parameter and Ω is a bounded domain in RN. We prove the existence of a large positive solution for λ large when limx → ∞ (f(Mg(x))/x) = 0 for every M > 0. In particular, we do not need any monotonicity assumptions on f, g, nor any sign conditions on f(0), g(0).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 1 , February 2004 , pp. 137 - 141
Copyright
Copyright © Royal Society of Edinburgh 2004