Tiago Praça Nunes Mexia
Universidade Nova de Lisboa, Portugal
João Tiago Praça Nunes Mexia was born in Lisbon in June of 1939. The most part of his career was as Full Professor at the FCT/UNL-Faculty for Sciences and Technology of the New University of Lisbon. At that time he supervised the teaching of Statistics at FCT/UNL and directed the Research Center in Mathematics of the University (CMA-Center for Mathematics and its Applications) from 1999 to 2009. In 2009 he became Emeritus Professor. Until now he supervised 19 Ph.D. and co-supervised 12 Ph.D. His research is centered on Linear Statistical Inference, having almost 100 papers published in International Journals.
National Academy of Sciences of Ukraine, Ukraine
Alexander Andreevych Boichuk is a Ukrainian mathematician, doctor of physical and mathematical sciences, professor, corresponding member of the National Academy of Sciences of Ukraine (since 2012), head of the laboratory boundary-value problems of differential equations of the Institute of Mathematics of the National Academy of Sciences of Ukraine, was awarded the State Prize of Ukraine in Science and Technology and Mitropolskiy Prize (2013). Professor A. Boichuk is an expert on the theory of the boundary value problems with the normally solvable operators in the linear part. For the first time defined the conditions for the solvability and spent the classification of the resonant cases a wide class of nonlinear boundary value problems for systems of ordinary differential and difference equations, delay equations, equations with impulsive and singularly perturbed equations for which the proposed use of the apparatus of generalized inverse operators. A. Boichuk is the author of over 110 scientific papers including three monographs. Under his guidance prepared 11 candidates of sciences.
Speech Title: "Boundary Value Problems of a Nonlinear Lyapunov Equation and Homoclinic Chaos"
Abstract: The report is devoted to obtaining a necessary and sufficient conditions of the existence of bounded on the whole axis solutions of a nonlinear evolution boundary value problems under assumption that corresponding homogeneous equation admits an exponential dichotomy on the semi-axes. We illustrate obtaining results for the Lyapunov type equation. We seek bounded solution of the nonlinear boundary value problem which turns in one of bounded solutions of the generating linear boundary value problem for the Lyapunov equation. It is shown that with using of proposed in report so called equation for generating operators we can obtain conditions of homoclinic chaos. We find connections between the well-known Palmer theorem and Melnikov function.