Solvability of Higher Order Iterative System with Non-Homogeneous Integral Boundary Conditions

The aim of this paper is to establish the existence positive solutions by determining eigenvalue intervals parameters μ1, μ2, ..., μm for iterative system nonlinear differential equations order p wi(p) (x) + μi ai fi (wi+1 ) = 0, 1 ≤ i m, x∈ [0,1], wm+1 w1 (x), x ∈ satisfying non-homogeneous integral boundary conditions wi (0) wi' wi(p-2) wi(r) - ηi ∫01gi(τ)wi(r)(τ)dτ λi, where r {1, 2, p−2} but fixed, ≥ 3 and ηi, λi (0, ∞) are parameters. fundamental tool in an application Guo-Krasnosel'skii fixed point theorem problem operators on a cone Banach space. Here kernels play role defining appropriate operator suitable cone.