Zhang Z. Variational, Topological, and Partial Order Methods with Their Applications

Springer, 2013. — 333 p. — (Developments in Mathematics 29). — ISBN10: 3642307086.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.Preliminaries
Cone and Partial Order Methods
Minimax Methods
Bifurcation and Critical Point
Solutions of a Class of Monge–Ampère Equations
Topological Methods and Applications
Dancer–Fučik Spectrum
Sign-Changing Solutions
Extension of Brezis–Nirenberg’s Results and Quasilinear Problems
Nonlocal Kirchhoff Elliptic Problems
Free Boundary Problems, System of Equations for Bose–Einstein Condensate and Competing Species