On a Class of Infinite Semipositone Nonlinear Systems with Multiple Parameters
<p>We analyze the existence of positive solutions of infinite semipositone nonlinear systems with multiple parameters of the form</p><span>{</span>Δu = α<sub>1</sub> (f (v)) - 1/<sub>u</sub><sup>n</sup>) + β<sub>1</sub>(h (u) - 1/<sub>u</sub><sup>n</sup>), x € Ω),<br /> -Δv = α<sub>2</sub> (g (u)) - 1/<sub>v</sub><sup>θ</sup>) + β<sub>2</sub>(k (v) - 1/<sub>u</sub><sup>θ</sup>), x € Ω), <br /> u = v = 0, x € δΩ),<p>where Ω is a bounded smooth domain of R<sup>N</sup>, η, θ ε (0, 1), and α<sub>1</sub>, α<sub>2</sub>, β<sub>1</sub> and β<sub>2</sub> are nonnegative parameters. Here f, g, h, k ε 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<sub>1</sub> + β<sub>1</sub> and α<sub>2</sub> + β<sub>2</sub> large.</p>