Variational, Topological, and Partial Order Methods with Their Applications (Developments in Mathematics) Hardcover
- Hardcover: 332 pages
- Author: Zhitao Zhang
- Publisher: Springer; 2013 edition (18 September 2012)
- Language: English
- ISBN-10: 9783642307089
- ISBN-13: 978-3642307089
- ASIN: 3642307086
- Product Dimensions: 16.5 x 2.5 x 24.8 cm
From the Back Cover
Nonlinear functional analysis is an important branch of contemporary mathematics. It’s related to topology, ordinary differential equations, partial differential equations, groups, dynamical systems, differential geometry, measure theory, and more. In this book, the author presents some new and interesting results on fundamental methods in nonlinear functional analysis, namely variational, topological and partial order methods, which have been used extensively to solve existence of solutions for elliptic equations, wave equations, Schrödinger equations, Hamiltonian systems etc., and are also used to study the existence of multiple solutions and properties of solutions. This book is useful for researchers and graduate students in the field of nonlinear functional analysis.
Chapter 1 contains preliminaries. In Chapter 2, three kinds of operators are introduced: increasing operators, decreasing operators, and mixed monotone operators. In Chapter 3, the minimax methods are presented and in Chapter 4, the author uses bifurcation and critical point theory to study structures of the solutions of elliptic equations. Chapter 5 is concerned with a class of Monge–Ampère equations. In Chapter 6, the superlinear system of Hammerstein integral equations and applications is studied. Chapter 7 is devoted to the Dancer–Fucik spectrum. In Chapter 8, some results on sign-changing solutions are introduced. In Chapter 9, a local minimizer problem of a functional in differential topology is studied. Chapter 10 focuses on a class of nonlocal Kirchhoff elliptic problems via different methods. In Chapter 11, the focus is on free boundary problems, Schrödinger systems from Bose–Einstein condensate and competing systems with many species.
About the Author
Zhitao Zhang is a professor at Academy of Mathematics and Systems Science. He was a Humboldt Research Fellow at Giessen University from June 2004 to June 2006. In 2011, he received a excellent advisor award of the Chinese Academy of Sciences. He mainly studies Nonlinear Analysis, Partial differential equations, Integral equations etc. He has published almost 50 papers in very important international journals such as Ann. Inst. H. Poincare Anal. Non Lineaire, J. Funct. Anal., Transactions of American Mathematical Society, J. Differential Equations etc. He has invited to write Chapter 13 for the Handbook of Nonconvex Analysis and Applications, International Press, 2010. His researches have been supported by Key program of National Natural Foundation of China. His papers have been cited by others more than 500 times. He was invited many times to present lectures at important international conferences.