IJPAM: Volume 72, No. 3 (2011)

ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF
HIGHER ORDER NONLINEAR DELAY IMPULSIVE
DIFFERENTIAL EQUATIONS WITH DAMPING

S. Pandian$^1$, G. Purushothaman$^2$
$^1$College of Arts and Science
Thiruvalluvar University
Vandavasi, Tamilnadu, INDIA
$^2$Department of Mathematics
St. Joseph's College of Engineering
Chennai, 119, Tamilnadu, INDIA


Abstract. In this paper, we investigated the sufficient conditions for asymptotic behavior of all solutions of higher order nonlinear delay impulsive differential equation of the form
\begin{gather*} \big(r(t)(x^{(2n-1)}(t))^\alpha \big)'+p(t)(x^{(2n-1)}(t))^\alp... ...{k}^{(i)}(x^{(i)}(t_k)),\quad i=0,1,2,\dots,2n-1,\ k=1,2,3\dots . \end{gather*}
Our results are extension of some known results.

Finally, we give an example to demonstrate our results.

Received: August 12, 2011

AMS Subject Classification: 34A37, 34K25

Key Words and Phrases: asymptotic behavior, higher order equation, impulsive differential equation

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2011
Volume: 72
Issue: 3