This book summarizes the qualitative theory of differential equations with or without delays, collecting recent oscillation studies important to applications and further developments in mathematics, physics, engineering, and biology. The authors address oscillatory and nonoscillatory properties of first-order delay and neutral delay differential equations, second-order delay and ordinary differential equations, higher-order delay differential equations, and systems of nonlinear differential equations. The final chapter explores key aspects of the oscillation of dynamic equations on time scales-a new and innovative theory that accomodates differential and difference equations simultaneously.
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Differential Equations
Mathematical Analysis
Reference
Professional

The qualitative theory of dynamic equations is a rapidly developing area of research. In the last 50 years, many scholars have studied the oscillation theory of ordinary, functional, neutral, partial, and impulsive differential equations. Many books deal with oscillation theory, but in a way that appeals only to researchers already familiar with the subject. In an effort to bring the topic to a new and broader audience, the authors clearly explain oscillation theory for second-order differential equations. They include several examples to illustrate the theory and to inspire new direction. This text is ideal for students and researchers in applied mathematics, engineering science, and numerical analysis.
• Mathematical Analysis and Applications
Differential Equations
Mathematical Analysis
Reference
Professional

Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
• Mathematical Analysis and Applications
Mathematical Analysis
Differential Equations
Applied Mathematics
Reference
Professional

A collection of 24 papers encompassing the construction and the qualitative as well as quantitative properties of solutions of Volterra, Fredholm amongst others.
• Mathematical Analysis and Applications
Differential Equations
Reference
Professional

A study of difference equations and inequalities. This second edition offers real-world examples and uses of difference equations in probability theory, queuing and statistical problems, stochastic time series, combinatorial analysis, number theory, geometry, electrical networks, quanta in radiation, genetics, economics, psychology, sociology, and other disciplines. It features 200 new problems, 400 additional references, and a new chapter on the qualitative properties of solutions of neutral difference equations.
• Pure and Applied Mathematics
Mathematical Analysis
Reference
Professional