Perturbed Fredholm boundary value problems for delay differential systems
Open Access
- 1 January 2003
- journal article
- research article
- Published by Hindawi Limited in Abstract and Applied Analysis
- Vol. 2003 (15), 843-864
- https://doi.org/10.1155/s1085337503304026
Abstract
Boundary value problems for systems of ordinary differential equations with a small parameterand with a finite number of measurable delays of the argument are considered. Under the assumption that the numberof boundary conditions does not exceed the dimensionof the differential system, it is proved that the pointgenerates-parametric families (where) of solutions of the initial problem. Bifurcation conditions of such solutions are established. Also, it is shown that the index of the operator, which is determined by the initial boundary value problem, is equal toand coincides with the index of the unperturbed problem. Finally, an algorithm for construction of solutions (in the form of Laurent series with a finite number terms of negative power of) of the boundary value problem under consideration is suggested.