The weakly perturbed $BVP’s$ for impulsive integro-differential systems areconsidered. Under the assumption that the generating problem(for $\varepsilon = 0 $) does not have solutions on the space$ W^1_2 [a, b] $ for some nonhomogeneities and using the Vishik-Lyusternik method, we establish conditions for the existence of solutions of these problems on the space $ D_2([a, b] \ { {\tau_i\} I } ) $ in the form of a Laurent series in powers of small parameter $\varepsilon $ with finitely many terms with negative powers of $\varepsilon $, and we suggest an algorithm of construction of these solutions.
@article{325,
title = {Weakly perturbed boundary-value problems for systems of integro-differential equations with impulsive action},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v63i0.325},
language = {EN},
url = {http://dml.mathdoc.fr/item/325}
}
Bondar, Ivanna. Weakly perturbed boundary-value problems for systems of integro-differential equations with impulsive action. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v63i0.325. http://gdmltest.u-ga.fr/item/325/