Equivariant Degree with Symmetric Nonlinear Boundary Value Problems

ISBN-13: 9783659453366 / Angielski / Miękka / 2014 / 104 str.

Nguyen My Linh

Opis

The Boundary value/periodic problems for the nonlinear equation (or, more generally, second order nonlinear ODEs) have been the focus of nonlinear analysis study for a long time. The goal of this book is to show how the equivariant degree theory can be used for the systematic study of multiple solutions to several (symmetric) generalizations of BVP and for the classification of symmetric properties of these solutions. There are several classical methods of nonlinear analysis used to solve the BVP. However, their application encounters serious difficulties if: the group of symmetries is large, the dimension of the problem is high, and multiplicities of eigenvalues of linearizations are large, etc. In this book, we: (i) set up the abstract functional analysis framework for studying symmetric properties of multiple solutions to symmetric generalizations of the BV problem via the equivariant degree approach; (ii) describe wide classes of second order BVPs admitting dihedral symmetries to which the abstract theory can be effectively applied; (iii) and apply the obtained results to several classes of implicit second order symmetric differential equations.

O autorze

My Linh Nguyen was born in Nha Trang, Vietnam. She attended at the University of Economics at HoChiMinh city with a major in Marketing Management. After 3 years, she immigrated to the United States. She studied at The University of Texas at Dallas with a Telecommunication Engineering major, earned her PhD in Applied Math, April 2013.