Liapunov Functionals for Integral Equations

This is an introduction to integral equations from the ground up. While it is elementary in nature, being accessible to advanced undergraduate mathematics majors, it introduces a number of problems of current research interest. The real distinguishing feature is that Liapunov's direct method is applied to the integral equation itself without first differentiating the equation. This is the first book to offer that topic and the ramifications are substantial.Basic linear and nonlinear theory is offered using elementary contraction mappings with extensive properties being derived from a substantial collection of Liapunov functionals. The linear methods advance in a natural way to nonlinear perturbations. Fixed point methods and Liapunov's direct method are woven together throughout the book.The book should be of interest to investigators in biology, chemistry, economics, engineering, mathematics, and physics.