Journal of Inequalities and Applications 
Volume 3 (1999), Issue 3, Pages 233-244
doi:10.1155/S1025583499000156

Differential inequalities with initial time difference and applications

V. Lakshmikantham1 and A. S. Vatsala2

 1Applied Math Program, Florida Institute of Technology, Melbourne 32901, FL, USA
2Department of Mathematics, University of Southwestern Louisiana, Lafayette 70504, LA, USA
Received 26 May 1998; Revised 6 July 1998

Abstract

The investigation of initial value problems of differential equations where the initial time differs with each solution is initiated in this paper. Basic preliminary results in qualitative theory are discussed to understand possible ramifications.