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.<\/o:p><\/span><\/p>Barnov\u2019s 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\u2019s approach. These changes among others include:<\/span><\/o:p><\/p> <\/span><\/p>\u00b7 <\/span><\/span>The addition of impulse effects on the dynamics of the system like impacts of impulses on the engine;<\/o:p><\/span><\/p>\u00b7 <\/span><\/span>Uniform treatment for delay and non-delay impulsive differential equations;<\/o:p><\/span><\/p>\u00b7 <\/span><\/span>Extension of Barnov\u2019s coordinate space model of impulses to phase state model where impulse may affect both the coordinates and the impulse momentum.<\/span><\/o:p><\/p> <\/span><\/p>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:<\/span><\/o:p><\/p> <\/span><\/p>\u00b7 <\/span><\/span>Precise formulation of the impulsive model with space state and system impulses;<\/o:p><\/span><\/p>\u00b7 <\/span><\/span>Formulation of condition for the existence of solutions and basic qualitative analysis of the solutions; and finally<\/o:p><\/span><\/p>\u00b7 <\/span><\/span>The study of asymptotic behaviour of delay and non-delay systems.<\/span><\/p><\/h2><\/div>\n\n\n\n\n\n\n\n\n\n\n
\n\n
\u00b7 \n<\/span><\/span>Z. Lipcsey, J. A. Ugbo, I.M. Esuabanga & <\/span>I. O. Isaac<\/span>\n(2020). Existence Theorem for Impulsive\nDifferential Equations with Measurable Right Side for Handling Delay\nProblems. Journal of Mathematics (Vol.\n2020),Article ID 7089313, 17 pages.<\/span><\/o:p><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipscey (2012). The Existence of Positive\nSolutions to Neutral Delay Impulsive Differential Equations. Communications in\nApplied Analysis 16 (1), 23 \u2013 46.<\/span><\/o:p><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span>, Z Lipcsey & UJ Ibok (2011).\nNonoscillatory and Oscillatory Criteria for First Order Nonlinear Neutral\nImpulsive Differential Equations. Journal of Mathematics Research 3 (2), 52 \u2013\n65. <\/o:p><\/span><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipscey (2010). Oscillations of\nScalar Neutral Impulsive Differential Equations of the First Order with\nVariable Coefficients. Dynamic Systems and Applications 19 (1), 45 \u2013 62.<\/o:p><\/span><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipscey (2010). Oscillations in\nLinear Neutral Delay Impulsive Deferential Equations with Constant\nCoefficients. Communications in Applied Analysis 14 (2), 123 \u2013 136. <\/o:p><\/span><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipcsey (2009). Linearized\nOscillations in Nonlinear Neutral Delay Impulsive Differential Equations.\nJournal of Modern Mathematics and Statistics 3 (1), 1 \u2013 7.<\/o:p><\/span><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipcsey (2009). Oscillations in\nnon-autonomous neutral impulsive differential equations with several delays.\nJournal of Modern Mathematics and Statistics 3 (4), 73 \u2013 77.<\/o:p><\/span><\/p>\n\n\u00b7 \n<\/span><\/span>IO Isaac<\/span> & Z Lipcsey (2009). Oscillations in\nSystems of Neutral Impulsive Differential Equations. Journal of Modern\nMathematics and Statistics 3 (1), 17 \u2013 21.<\/span><\/o:p><\/p><\/h2>\n\n\n\n\n\n\n\n\n\n\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"pagelayer_contact_templates":[],"_pagelayer_content":"","footnotes":""},"class_list":["post-946","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/pages\/946","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/comments?post=946"}],"version-history":[{"count":7,"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/pages\/946\/revisions"}],"predecessor-version":[{"id":953,"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/pages\/946\/revisions\/953"}],"wp:attachment":[{"href":"https:\/\/aksu.edu.ng\/newsite\/wp-json\/wp\/v2\/media?parent=946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}