UID:
almahu_9949698058502882
Format:
1 online resource (360 p.)
ISBN:
1-4832-7837-9
Series Statement:
Studies in Applied Mechanics ; 2
Content:
Nonlinear Differential Equations
Note:
Description based upon print version of record.
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Front Cover; Nonlinear Differential Equations; Copyright Page; Table of Contents; PREFACE; 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
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Section 10. Solution of a Boundary Value ProblemSection 11. On an Integral Identity; CHAPTER III. THE WEAK SOLUTION OF A BOUNDARY VALUE PROBLEM; Section 12. The Carathéodory Property and the NФеmyckiéǐ 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
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Section 21. Second Derivative of a FunctionalSection 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
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CHAPTER VI. NONCOERCIVE PROBLEMSSection 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; REFERENCES; INDEX
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English
Additional Edition:
ISBN 1-322-46500-2
Additional Edition:
ISBN 0-444-41758-3
Language:
English
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