Proceedings of the Royal Society of Edinburgh: Section A Mathematics

Research Article

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

D. D. Haia1 and R. Shivajia2

a1 Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA (dang@math.msstate.edu)

a2 Department of Mathematics, Mississippi State University, Mississippi State, MS 39762, USA (shivaji@msstate.edu)

Abstract

Consider the system

S0308210500003115disp001

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).

(Received December 03 2002)

(Accepted May 06 2003)