As a very important part of nonlinear analysis, fixed point theory plays a key role in solvability of many complex systems from mathematics applied to chemical reactors, neutron transport, population biology, infectious diseases, economics, applied mechanics, and more.

The main aim of Fixed Point Theorems with Applications is to explain new techniques for investigation of different classes of ordinary and partial differential equations. The development of the fixed point theory parallels the advances in topology and functional analysis. Recent research has investigated not only the existence but also the positivity of solutions for various types of nonlinear equations. This book will be of interest to those working in functional analysis and its applications.

Combined with other nonlinear methods such as variational methods and the approximation methods, the fixed point theory is powerful in dealing with many nonlinear problems from the real world.

The book can be used as a textbook to develop an elective course on nonlinear functional analysis with applications in undergraduate and graduate programs in mathematics or engineering programs.

chapter Chapter 1|148 pages


chapter Chapter 2|42 pages

Fixed-Point Index for Sums of Two Operators

chapter Chapter 3|40 pages

Positive Fixed Points for Sums of Two Operators

chapter Chapter 4|70 pages

Applications to ODEs

chapter Chapter 5|50 pages

Applications to Parabolic Equations

chapter Chapter 6|66 pages

Applications to Hyperbolic Equations