## Abstract

We consider the integral boundary value problem (BVP) for a certain class of non-linear system of ordinary differential equations of the form (Formula Presented) where (Formula Presented) and t ∈ [0,T], x ∈ ℝ^{n}, f : [0,T] × D → ℝ ^{n} and k : [0-T] × → ℝ ^{n} are continuous vector functions, D ⊂ ℝ^{n} is a closed and bounded domain, A, C and d are arbitrary matrices and vector with real components, det C ≠ 0. We give a new approach for studying this problem, namely by using an appropriate parametrization technique the original BVP is reduced to the equivalent parametrized two-point one with linear restrictions without integral term. To study the transformed problem we use a method based upon a special type of successive approximations constructed analytically.

Original language | English |
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Journal | Electronic Journal of Qualitative Theory of Differential Equations |

Volume | 2016 |

DOIs | |

Publication status | Published - 1 Jan 2016 |

Externally published | Yes |

## Keywords

- Integral boundary value problems
- Numerical–analytic technique
- Parametrization
- Successive approximations