"Differential Equations: Theory and Current Research" ed. by Terry E. Moschandreou

This volume is incorporated contributions from a diverse group of leading researchers in the field of differential equations. This book aims to provide an overview of the current knowledge in the field of differential equations. The book is written primarily for those who have some knowledge of differential equations and mathematical analysis.


The main subject areas are divided into general theory and applications. These include fixed point approach to solution existence of differential equations, existence theory of differential equations of arbitrary order, topological methods in the theory of ordinary differential equations, impulsive fractional differential equations with finite delay and integral boundary conditions, an extension of Massera's theorem for n-dimensional stochastic differential equations, phase portraits of cubic dynamic systems in a Poincare circle, differential equations arising from the three-variable Hermite polynomials and computation of their zeros and reproducing kernel method for differential equations. Applications include local discontinuous Galerkin method for nonlinear Ginzburg-Landau equation, general function method in transport boundary value problems of theory of elasticity and solution of nonlinear partial differential equations by new Laplace variational iteration method. Existence/uniqueness theory of differential equations is presented in this book with applications that will be of benefit to mathematicians, applied mathematicians and researchers in the field.


Contents
1 Fixed Point Theory Approach to Existence of Solutions with Differential Equations
2 Existence Theory of Differential Equations of Arbitrary
3 An Extension of Massera's Theorem for N-Dimensional Stochastic Differential Equations
4 Phase Portraits of Cubic Dynamic Systems in a Poincare Circle
5 Differential Equations Arising from the 3-Variable Hermite Polynomials and Computation of Their Zeros
6 Reproducing Kernel Functions
7 Local Discontinuous Galerkin Method for Nonlinear Ginzburg-Landau Equation
8 General Functions Method in Transport Boundary Value Problems of Elasticity Theory
9 Solution of Nonlinear Partial Differential Equations by New Laplace Variational Iteration Method