Plenary Lecture

On Qualitative Properties and Asymptotic Behavior of Solutions to Higher-Order Nonlinear Differential Equations

Professor Irina V. Astashova
Faculty of Mechanics and Mathematics
Lomonosov Moscow State University

Abstract: This talk is devoted to the asymptotic behavior of solutions to some higher-order generalizations of the Emden-Fowler equation. Several author's results will be presented concerning both positive and oscillatory solutions to equations with regular and singular nonlinearities.
We will discuss the existence and asymptotic behavior of "blow-up", "black hole", and "white hole" solutions. For slightly different equations, the asymptotic equivalence of their positive vanishing solutions will be discussed. An oscillation criterion and some results on the asymptotic behavior of oscillating solutions will be formulated. For the second-, third-, and forth-order equations, an asymptotic classification of the solutions will be presented. Some applications of the results obtained will be proposed.

Brief Biography of the Speaker: Irina Astashova (, Full Professor of Lomonosov Moscow State University, Fa-culty of Mechanics and Mathematics, dept. of Differential Equations, Professor of Plekhanov Russian University of Economics, Faculty MESI. Education: Lomonosov Moscow State University, faculty of Mechanics and Mathematics (1978), Post-graduate in 01.01.02 (“Differential Equations”), Lomonosov Moscow State University (1984) Ph.D. in 01.01.02 (“Differential Equations”); thesis: “Asymptotic Properties of Solutions to Some Nonlinear Differential Equations”( 1989.) Doctor of Physics and Mathematics, thesis: «Qualitative properties of solutions to quasilinear ordinary differential equations» (2008) Teaching Experience: Assistant Professor, Moscow Technical University of Communications and Informatics (MTUCI) (1977-1992); Associated Professor, Moscow Aviation Technology University (MATI) (1992-2002); Associated Professor, after 2005 professor, Moscow State University of Economics, Statistics, and Informatics (MESI) (1992-2015); Professor, Lomonosov Moscow State University (2008 up to now); Professor, Plekhanov Russian University of Economics, faculty MESI (2015 up to now). Courses given: Differential Equations, Partial Differential Equations, Functional Analysis, Com-plex Analysis, Geometry and Topology, Qualitative Theory of Differential Equations for students and post-graduates. Seminars: Head of a scientific Seminar on qualitative theory of differential equations, Mos-cow Aviation Technology University (MATI) (1994-2002), of Seminar on qualitative theory of differential equations, Lomonosov Moscow State University (2009 up to now), of Interuni-versity Seminar on qualitative theory of differential equations and related topics (Lomonosov MSU - Bauman MGTU - Plechanov REU (MESI)) ( 2002 up to now). Publications: more than 100 articles, 7 monographs. Societies: Member of Moscow Mathematical Society since 1989, Member of European Mathe-matical Society since 2015. Award: Keldysh medal of the Russian Cosmonautics Federation.

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