George E. Chatzarakis, Kusano Takasi, Ioannis P. Stavroulakis
Abstract:
In this article, we study the asymptotic behavior of strongly decreasing
solutions of the first-order nonlinear functional differential equation
where
is a positive constant such that
,
p(t) is a
positive continuous function on
,
a>0 and g(t) is a
positive continuous function on
such that
. Conditions which guarantee the existence
of strongly decreasing solutions are established, and theorems are stated on the
asymptotic behavior of such solutions, at infinity. The problem it is
studied in the framework of regular variation, assuming that the coefficient
p(t) is a regularly varying function, and focusing on strongly decreasing
solutions that are regularly varying. In addition, g(t) is required to
satisfy the condition
Examples illustrating the results are also given.
Submitted June 26, 2014. Published October 2, 2014.
Math Subject Classifications: 34C11, 26A12
Key Words: Functional differential equation; strongly decreasing solution;
regularly varying function; slowly varying solution.
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George E. Chatzarakis Department of Electrical and Electronic Engineering Educators School of Pedagogical and Technological Education (ASPETE) 14121, N. Heraklio, Athens, Greece email: geaxatz@otenet.gr, gea.xatz@aspete.gr | |
Kusano Takasi Professor Emeritus at: Department of Mathematics Faculty of Science, Hiroshima University Higashi-Hiroshima 739-8526, Japan email: kusanot@zj8.so-net.ne.jp | |
Ioannis P. Stavroulakis Department of Mathematics, University of Ioannina 451 10 Ioannina, Greece email: ipstav@cc.uoi.gr |
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