Perturbed Fredholm BVP's for systems of delay differential equations
by
Alexander Boichuk
University of Zilina, Slovak Republic and Institute of Mathematics NAS of Ukraine

Boundary value problems for systems of ordinary differential equations with a small parameter \epsilon and with a finite number of measurable delays

× z   (t)= k å i=1  Ai(t)z(hi(t))+\epsilon k å i=1  Bi(t)z(hi(t))+g(t),     t in [a, b],   hi(t) <= t,

z(s)=\psi(s),   if  s < a < b,     lz=\alpha in Rm

are considered in corresponding Banach spaces . Under the assumption that the number m of boundary conditions not exceeds the dimension n of the differential system, it is proved that the point \epsilon = 0  generates \rho =(n-m) - parametric families of solutions of the initial problem for arbitrary nonhomogeneities . 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 to  \rho  and coincides with the index of the unperturbed problem. Finally, an algorithm for construction of solutions of the boundary value problem under consideration is suggested. Research supported by grant VEGA 1/0026/03 of Slovak Grant Agency.

Date received: May 14, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # calh-36.