Nonlinear Differential Equations

Svatopluk Fucik, Alois Kufner

• Publisher: Elsevier
• Year: 2014
• Print ISBN: 9780444417589
• eBook ISBN: 9781483278377
• Topic: Technology & Engineering
• Subtopic: Engineering General
• Index: Technology & Engineering

Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

Table of contents

• Front Cover
• Nonlinear Differential Equations
• Copyright Page
• Table of Contents
• PREFACE
• LIST OF SYMBOLS
• CHAPTER I. SOME EXAMPLES TO BEGIN WITH
• CHAPTER II. INTRODUCTION
• CHAPTER III. THE WEAK SOLUTION OF A BOUNDARY VALUE PROBLEM
• CHAPTER IV. THE VARIATIONAL METHOD
• CHAPTER V. THE TOPOLOGICAL METHOD
• CHAPTER VI. NONCOERCIVE PROBLEMS
• CHAPTER VII. VARIATIONAL INEQUALITIES
• REFERENCES
• INDEX