About DEAN

prof isaac

Prof. Idongesit O. Isaac

Dean Physical Sciences

Dean's Profile

I am a Professor of Mathematics in Akwa Ibom State University, Ikot Akpaden, Mkpat Enin L.G.A., Akwa Ibom State. My professional life includes working as a writer, an editor, a fabricator and as well a mathematician. I received my Ph. D. in 2007 from the University of Calabar and have taught for several years in the same institution before transferring my service to Akwa Ibom State University. Other institutions I have taught include University of Uyo and Maritime Academy Oron. I am especially interested in Integral Equations, Oscillation Theory for Impulsive Differential Equations and related areas in analysis.


·         Doctor of Philosophy (Ph. D.), Applied Mathematics, University of Calabar, 2007.

·         Master of Science (M. Sc.), Mathematical Physics, Kharkov State University (USSR), 1986.

Professional Memberships and Activities

·         Nigerian Mathematical Society.

·         Nigerian Statistical Society.

·         Institute for Operations Research of Nigeria.


·         TWAS Sponsored Project: Numerical Solutions to Singular Integral Equations of the second kind with real and with complex coefficients.

·         Impulsive Differential Equations: Oscillation Theory for Neutral Delay Impulsive Differential Equations.

Contact Details:

Email:                          idongesitisaac@aksu.edu.ng, idonggrace@yahoo.com

Telephone number:     +234(0)8056138778, +234(0)8122874958

Postal Address:           Department of Mathematics

Akwa Ibom State University

P.M.B. 1167, Uyo.

Akwa Ibom State, Nigeria.

Research Interest

Impulsive differential equations describe processes with dynamics of differential equations combined with quick impacts caused by indefinite events. This circle of problems plays an important role in real life since in any design, there are unexpected events. Stochastic differential equations discuss these problems among others in modelling statistical mechanics. It was Barnov and his associates who first formulated the deterministic model of the impact of impulse effects on systems.

Barnov’s initiatives had a strong influence on the research direction in all the countries that embraced the concept. Consequently, some fundamental aspects of research areas which play important role in such applications as the treatment of delay equations and some other fields missed certain valuable points. There is need to develop a new formulation of the problem that contains the whole Barnovian theory and addresses the circle of problems missing in Barnov’s approach. These changes among others include:


·         The addition of impulse effects on the dynamics of the system like impacts of impulses on the engine;

·         Uniform treatment for delay and non-delay impulsive differential equations;

·         Extension of Barnov’s coordinate space model of impulses to phase state model where impulse may affect both the coordinates and the impulse momentum.


It is worthy of note that the framework of functions of bounded variation gives a chance to build together the coordinate space impulses with the impulses on the system dynamics into a consistent system. The approach is expected to offer a unified frame to handle delay/non-delay problems with the ease similar to what happens in the theory of conventional differential equations. My study aims at the following:


·         Precise formulation of the impulsive model with space state and system impulses;

·         Formulation of condition for the existence of solutions and basic qualitative analysis of the solutions; and finally

·         The study of asymptotic behaviour of delay and non-delay systems.

Selected Publication

·        Z. Lipcsey, J. A. Ugbo, I.M. Esuabanga & I. O. Isaac (2020).  Existence Theorem for Impulsive Differential Equations with Measurable Right Side for Handling Delay Problems.  Journal of Mathematics (Vol. 2020),Article ID 7089313, 17 pages.

·         IO Isaac & Z Lipscey (2012). The Existence of Positive Solutions to Neutral Delay Impulsive Differential Equations. Communications in Applied Analysis 16 (1), 23 – 46.

·         IO Isaac, Z Lipcsey & UJ Ibok (2011). Nonoscillatory and Oscillatory Criteria for First Order Nonlinear Neutral Impulsive Differential Equations. Journal of Mathematics Research 3 (2), 52 – 65.

·         IO Isaac & Z Lipscey (2010). Oscillations of Scalar Neutral Impulsive Differential Equations of the First Order with Variable Coefficients. Dynamic Systems and Applications 19 (1), 45 – 62.

·         IO Isaac & Z Lipscey (2010). Oscillations in Linear Neutral Delay Impulsive Deferential Equations with Constant Coefficients. Communications in Applied Analysis 14 (2), 123 – 136. 

·         IO Isaac & Z Lipcsey (2009). Linearized Oscillations in Nonlinear Neutral Delay Impulsive Differential Equations. Journal of Modern Mathematics and Statistics 3 (1), 1 – 7.

·         IO Isaac & Z Lipcsey (2009). Oscillations in non-autonomous neutral impulsive differential equations with several delays. Journal of Modern Mathematics and Statistics 3 (4), 73 – 77.

·         IO Isaac & Z Lipcsey (2009). Oscillations in Systems of Neutral Impulsive Differential Equations. Journal of Modern Mathematics and Statistics 3 (1), 17 – 21.