Linearized Oscillations in Autonomous Delay Impulsive Differential Equations
I. O. Isaac *
Department of Mathematics/Statistics and Computer Science, University of Calabar, P.M.B. 1115, Calabar, Cross River State, Nigeria.
Z. Lipcsey
Department of Mathematics/Statistics and Computer Science, University of Calabar, P.M.B. 1115, Calabar, Cross River State, Nigeria.
U. J. Ibok
Department of Pure and Applied Chemistry, University of Calabar P.M.B. 1115, Calabar, Cross River State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In recent years, there have been intensive efforts to establish linearised oscillation results for onedimensional delay, neutral delay and advanced impulsive differential equations. An impressive number of these efforts have yielded fruitful results in many analytical and applied areas. This is particularly obvious in the areas of applied disciplines such as the linear delay impulsive differential equations. However, there still remains a lot more to be explored in this direction, especially, in the area of non-linear autonomous differential equations. In this paper, we are proposing the development of linearised oscillation techniques for some general non-linear autonomous impulsive differential equations with several delays.
Keywords: Linearised oscillation, Delay impulsive differential equations.