Constructive existence analysis of solutions of non-linear integral boundaryvalue problems

Abstract

Sufficient conditions guaranteeing the solvability of non-linear integral boundary value problems for a system of non-linear ordinary differential equations are obtained using a special successive approximation technique. The efficiency of the suggested approach is shown on an example of a non-linear integral boundary value problem possessing at least two solutions.

On investigation of some non-linear integral boundary value problem

“…Note, that similarly as in [3], the solvability of the determining system (2.9) on the base of (1.3)-(1.5) and (1.9) can be established by studying its m th approximate versions: is a solution of the non-linear boundary value problem (1.1)-(1.2).…”