Objective
A number of innovative problems which should form the basis for new directions in the development of general theory of impulsive differential equations will be studied. Besides of significant theoretical importance of the proposal, it may also have a number of important applications related primarily to control theory (e.g. impulsive control of various evolution systems, continuous or impulsive control in impulsive systems), mathematical modeling of biological systems (e.g. harvesting or heavy immigration in population dynamics), etc. Existence of almost periodic solutions to abstract impulsive evolution systems and impulsive partial differential equations of parabolic type will be studied. Algorithms and software for approximate construction of rrrent and quasi-periodic solutions will be given. Constructive existence results for initial and boundary value problems for a variety of nonlinear equations will be proved by using the method of upper and lower solutions with the monotone iterative technique. Stability, dichotomy, bifurcation, beating of solutions to different classes of impulsive systems will be studied. Discontinuous invariant tori corresponding to multi-frequency oscillations and a linearized system in the neighborhood of invariant set will be considered. Various boundary value problems for nonlinear second-order impulsive systems will be investigated. A number of qualitative properties of solutions of delay impulsive differential equations such as existence, continuous dependence on initial data and parameters, stability of solutions will be studied. Applications to control theory and mathematical biology will be considered. It is planned to organize in Kyiv an international conference on impulsive differential equations in 1999.
Topic(s)
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60000 Beauvais
France