On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters

Abstract

We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form {Δu = α 1 (f (v)) - 1/ u n ) + β 1 (h (u) - 1/ u n ), x € Ω), -Δv = α 2 (g (u)) - 1/ v θ ) + β 2 (k (v) - 1/ u θ ),  x € Ω), u = v =0,  x € δΩ), where Ω is a bounded smooth domain of R N , η, θ e (0, 1), and α 1 , α 2 , β 1 and β 2 are nonnegative parameters. Here f, g, h, k e C ([0, ∞ ]), are non-decreasing functions and f(0), g(0), h(0), k(0) > 0. We use the method of sub-super solutions to prove the existence of positive solution for α 1 + β 1 and α 2 + β 2 large.