International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 365-372
doi:10.1155/S0161171286000455

Analytic solutions of nonlinear neutral and advanced differential equatios

Joseph Wiener,1 Lokenath Debnath,2 and S. M. Shah3

1Department of Mathematics, Pan American University, Edinburg 78539, Texas, USA
2Department of Mathematics, University of Central Florida, Orlando 32816, Florida, USA
3Department of Mathematics, University of Kentucky, Lexington 40506, Kentucky, USA

Received 15 May 1985

Copyright © 1986 Joseph Wiener 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.

Abstract

A study is made of local existence and uniqueness theorems for analytic solutions of nonlinear differential equations of neutral and advanced types. These results are of special interest for advanced eauations whose solutions, in general, lose their margin of smoothness. Furthermore, existence of entire solutions is established for linear advanced differential systems with polynomial coefficients.