On the Existence of Positive Solutions for a Class of Infinite Semipositone Systems with Singular Weights: S.H. Rasouli
In this paper we consider the existence of positive solutions of infinite semipositone systems with singular weights of the form {arrayll -div(|x|^-ap | abla u|^p-2 abla u) = λ |x|^-(a+1)p+c_1 (f(v)-1u^α ), & xΩ, -div(|x|^-bq | abla v|^q-2 abla v) = λ |x|^-(b+1)q+c_2 (g(u)-1v^β ), & xΩ, u = 0 =v, & xΩ, array. where Ω is a bounded smooth domain of R^N with 0Ω, 1<p,q<N, 0≤ a<N-pp, 0≤ b<N-qq, α, β (0,1), and c_1,c_2,λ are positive parameters. Here f,g:(0,∞)→ (0,∞) are C^2 functions. Our aim in this paper is to establish the existence of positive solution for λ large. We use the method of sub-super solutions to establish our existence result. , number=1, journal=Thai Journal of Mathematics, author=Team, Support, year=2013, month=Apr., pages=103–110