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The project is devoted to further development of the theory of the summation integration and its application to generalized ordinary differential equations (ODE) and consequently to various types of classical differential equations. Our aim is to continue the study of summation integrals of the Henstock-Kurzweil type of functions with values in a Banach space and to create a new unified theory of generalized ODE's which should cover both the cases of fastly oscillating right hand sides of an ODE and the case of an ODE of Carathéodory type. The signification of our project consists in the further development of the qualitative theory of ordinary and functional differential equations. We expect new results concerning the general summation integral and its applications in the theory of differential and integral equations. Our goal is to continue and to unify in many aspects the results obtained until now. We are planning a new book devoted to generalized ODE's in Banach spaces.
Main investigators:
Participating institutions:
Institute of Mathematics AS CR
