IJPAM: Volume 46, No. 2 (2008)

Invited Lecture Delivered at
Forth International Conference of Applied Mathematics
and Computing (Plovdiv, Bulgaria, August 12-18, 2007)


ON THE EXISTENCE AND THE ASYMPTOTIC BEHAVIOUR
OF REGULARLY (SLOWLY) VARYING SOLUTIONS OF SOME
CLASSES OF SECOND ORDER FUNCTIONAL DIFFERENTIAL
EQUATIONS WITH DEVIATING ARGUMENT

Kusano Takasi$^1$, Vojislav Maric$^2$
$^1$Department of Applied Mathematics
Faculty of Science
Fukuoka University
Fukuoka, 841-0180, JAPAN
e-mail: tkusano@cis.fukuoka-u.ac.jp
$^2$Serbian Academy of Sciences and Arts
Kneza Mihaila 35, Beograd, 11000, SERBIA
e-mail: vojam@uns.ns.ac.yu


Abstract.Functional differential equations of the second order with deviating arguments are studied in the framework of Karamata regularly varying functions. Sharp conditions are established for the existence of slowly and regularly varying solutions. Some results on the asymptotics of these solutions are also given.

Received: August 17, 2007

AMS Subject Classification: 34K06, 26A12

Key Words and Phrases: functional differential equations, deviating arguments, slowly, regularly varying functions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 2