This Research Note introduces a new Morse (index) theory that is easie r to use, less technical, and more flexible than existing theories. Un til now, these results have appeared only in scattered journals. The a uthor provides a self-contained treatment with full proofs of the majo r results and complete with applications of the theory to Hamiltonian systems and other areas of current research, including wave equations, Chern-Simon functionals, and Lorentzian geometry

This book analyzes the existence and uniqueness of a generalized algebraic m- tiplicity for a general one-parameter family L of bounded linear operators with Fredholm index zero at a value of the parameter ? whereL(? ) is non-invertible. 0 0 Precisely, given K?{R, C}, two Banach spaces U and V over K, an open subset ? ? K, andapoint ? ? ?, our admissible operator families are the maps 0 r L?C (?, L(U, V)) (1) for some r? N, such that L(? )? Fred (U, V); 0 0 hereL(U, V) stands for the space of linear continuous operatorsfrom U to V, and Fred (U, V) is its subset consisting of all Fredholm...

Analyze Global Nonlinear Problems Using Metasolutions

Metasolutions of Parabolic Equations in Population Dynamics explores the dynamics of a generalized prototype of semilinear parabolic logistic problem. Highlighting the author s advanced work in the field, it covers the latest developments in the theory of nonlinear parabolic problems.

The book reveals how to mathematically determine if a species maintains, dwindles, or increases under certain circumstances. It explains how to predict the time evolution of species inhabiting regions...