Journal of Applied Mathematics and Stochastic Analysis
Volume 2004 (2004), Issue 3, Pages 261-270

A singular initial value problem for some functional differential equations

Ravi P. Agarwal,1 Donal O'Regan,2 and Oleksandr E. Zernov3

1Department of Mathematical Sciences, Florida Institute of Technology, Melbourne 32901, FL, USA
2Department of Mathematics, National University of Ireland, Galway, Ireland
3South Ukrainian State Pedagogical University, Odessa, Ukraine

Received 3 May 2004; Revised 13 May 2004

Copyright © 2004 Ravi P. Agarwal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


For the initial value problem trx(t)=at+b1x(t)+b2x(q1t)+b3trx(q2t)+φ(t,x(t),x(q1t),x(t),x(q2t)), x(0)=0, where r>1, 0<qi1, i{1,2}, we find a nonempty set of continuously differentiable solutions x:(0,ρ], each of which possesses nice asymptotic properties when t+0.