Some classes of second order functional differential equations

✍ Scribed by C. Corduneanu

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 302 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2008.12.027

✦ Synopsis

This paper is dedicated to the concise presentation of some results (mainly, existence theorems and behavior of solutions) related to functional differential equations of the form

in which L stands for a linear operator on a certain function space, causal and continuous, while V is acting on the same function space, but it is assumed only causal and continuous (in general, nonlinear). We provide several existence results, under various assumptions. Also, we show that, under extra conditions, the solutions can present various types of behavior on a semi-axis, or on the whole real axis. Some applications are indicated, and references are provided.

The results have been obtained by the author and his former students Mehran Mahdavi and Yizeng Li, during the last ten years. Some results are published here for the first time. An earlier account of these kind of problems is given in [C.