Existence of positive solutions for nonlinear dynamic systems with a parameter on a measure chain

Abstract

In this paper, we consider the following dynamic system with parameter on a measure chain T, uiΔΔ(t) + λhi(t)ƒi(u1(σ(t)), u2(σ(t)),..., un(σ(t))) = 0, t ∈ [ɑ, b], ɑui(ɑ) - βu1Δ(ɑ) = 0, γui(σ(b)) + δuiΔ (σ(b)) = 0, where i = 1, 2,..., n. Using fixed point index theory, we find sufficient conditions the existence of positive solutions.