Abstract
The cone theory together with Monch fixed point theorem and a monotone iterative technique is used to investigate the positive solutions for some boundary problems for systems of nonlinear second-order differential equations with multipoint boundary value conditions on infinite intervals in Banach spaces. The conditions for the existence of positive solutions are established. In addition, an explicit iterative approximation of the solution for the boundary value problem is also derived.
Highlights
In recent years, the theory of ordinary differential equations in Banach space has become a new important branch of investigation see, e.g., 1–4 and references therein
By employing a fixed point theorem due to Sadovskii, Liu 5 investigated the existence of solutions for the following second-order two-point boundary value problems BVP for short on infinite intervals in a Banach space E: x t f t, x t, x t, t ∈ J, 1.1 x 0 x0, x ∞ y∞, where f ∈ C J ×E×E, E, J 0, ∞, x ∞ limt → ∞x t
By using Shauder fixed point theorem, Guo 15 obtained the existence of positive solutions for a class of nth-order nonlinear impulsive singular integro-differential equations in a Banach space
Summary
The theory of ordinary differential equations in Banach space has become a new important branch of investigation see, e.g., 1–4 and references therein. By employing a fixed point theorem due to Sadovskii, Liu 5 investigated the existence of solutions for the following second-order two-point boundary value problems BVP for short on infinite intervals in a Banach space E:. We consider the following singular m-point boundary value problem on an infinite interval in a Banach space E x t f t, x t , x t , y t , y t 0, y t g t, x t , x t , y t , y t 0, t ∈ J , m−2. By using Shauder fixed point theorem, Guo 15 obtained the existence of positive solutions for a class of nth-order nonlinear impulsive singular integro-differential equations in a Banach space.
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