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Nonlinear Differential Equations - 1st Edition - ISBN: 9780444417589, 9781483278377

Nonlinear Differential Equations, Volume 2

1st Edition

Authors: Svatopluk Fucik Alois Kufner
eBook ISBN: 9781483278377
Imprint: Elsevier
Published Date: 1st January 1980
Page Count: 360
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Table of Contents


List of Symbols

Chapter I. Some Examples to Begin with

Section 1. Various Notations. Linear Equations

Section 2. Nonlinear Equations

Section 3. Nonlinear Systems

Section 4. Further Nonlinear Problems

Section 5. A Free Boundary Problem. The Plate Equation

Chapter II. Introduction

Section 6. Second Order Equations

Section 7. Higher Order Equations

Section 8. Spaces of Continuous Functions. Solution of a Differential Equation

Section 9. Boundary Conditions

Section 10. Solution of a Boundary Value Problem

Section 11. On an Integral Identity

Chapter III. The Weak Solution of a Boundary Value Problem

Section 12. The Carathéodory Property and the Němyckiĭ Operators

Section 13. Sobolev Spaces

Section 14. Differential Operators

Section 15. Boundary Value Problems

Section 16. Various Generalizations

Section 17. Regularity of the Weak Solution

Chapter IV. The Variational Method

Section 18. First Derivative of a Functional

Section 19. Potentials of Boundary Value Problems

Section 20. The Euler Necessary Condition

Section 21. Second Derivative of a Functional

Section 22. Lagrange Conditions

Section 23. Convex Functionals

Section 24. Weak Convergence and Weak Compactness

Section 25. Reflexive Spaces

Section 26. Existence Theorems

Section 27. Minimal Surfaces

Section 28. Excursion on Numerical Methods

Chapter V. The Topological Method

Section 29. Existence Theorems

Section 30. The Brouwer and the Leray-Schauder Degree of a Mapping

Section 31. General Boundary Conditions for Second Order Ordinary Differential Equations

Section 32. Summary of Chapters IV and V. Some Additional Remarks

Chapter VI. Noncoercive Problems

Section 33. Vanishing Nonlinearities. Regular Case

Section 34. Vanishing Nonlinearities. Singular Case

Section 35. Jumping Nonlinearities with Finite Jumps

Section 36. Jumping Nonlinearities with Infinite Jumps

Section 37. Rapid Nonlinearities

Section 38. Periodic Problems

Chapter VII. Variational Inequalities

Section 39. Formulation of the Problem

Section 40. More on the Definition of the Solution of a Variational Inequality

Section 41. Examples

Section 42. Some Special Results

Section 43. Existence Theorems




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.


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© Elsevier 1980
1st January 1980
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About the Authors

Svatopluk Fucik

Alois Kufner