Plenary Lecture

Topological Methods for Higher Order Nonlinear Impulsive Boundary Value Problems

Professor Feliz Minhós
Departament of Mathematics
University of Évora
Portugal
E-mail: fminhos@uevora.pt

Abstract: The theory of impulsive problems is well adapted to study real phenomena where sudden changes occur at certain moments. Several examples arise naturally, not only on a micro scale but also on a global level, in physics, medicine, biotechnology, economics, control theory, population and/or gene dynamics,...This theory has become an increasingly important field in in research and it has been combined with different methods, boundary conditions and several interpretations for the impulse conditions.
This presentation will include two types of boundary and impulsive conditions:
A fourth-order periodic impulsive problem with a fully differential equation, that is, where the nonlinearity can depend in every derivatives till the third order, and the impulsive effects, are given by general functions, not necessarily linear. The main argument to obtain the existence of solutions is based in an iterative technique, not necessarily monotone;
A three point impulsive boundary value problem, which higher order contains an increasing homeomorphism, and where the impulsive functions are given via multivariate generalized functions, including impulses on the referred homeomorphism.
The method used apply lower and upper solutions technique together with fixed point theory. Therefore we have not only the existence of solutions but also the localization and qualitative data on their behavior. Moreover a Nagumo condition will play a key role in the arguments.

Brief Biography of the Speaker: Feliz Manuel Minhós is a Professor in the Department of Mathematics, School of Sciences and Technology, University of Évora, PORTUGAL, and researcher in the Research Center in Mathematics and Applications of the University of Évora. He obtained a PhD in Mathematics in the University of Évora, Portugal, in 2002, and the Habilitation degree, by the same university in 2010. Prof. Minhós has a vast experience in different areas of Nonlinear Analysis, such as variational and topological methods for Boundary Value Problems, topological degree, fixed point theory, lower and upper solutions method, Mountain Pass theory, etc. He has published 1 scientific book, 52 papers in international journals, 5 pedagogical books for undergraduate students, presented many communications in international meetings all around the world and won several awards granted by Foundation for Science and Technology, Calouste Gulbenkian Foundation, Portuguese-American Foundation, CRUP, and by private enterprises. In his work there are collaborations in several projects with colleagues of Spain, USA, Italy, Bulgaria, Bahamas, Israel,… He is member of the editorial board of several International Journals, Guest Editor of 3 Special Issues, Reviewer of Mathematical Reviews. He is adviser of 3 PhD thesis ongoing and two already concluded.

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