Author(s): Svatopluk Fucik
Series: Studies in Applied Mechanics
Publisher: Elsevier Science Ltd
Year: 1980
Language: English
Pages: 358
Tags: Математика;Дифференциальные уравнения;
Contents......Page 4
Preface......Page 6
List of symbols......Page 10
1. Various Notations. Linear Equations......Page 14
2. Nonlinear Equations......Page 18
3. Nonlinear Systems......Page 23
4. Further Nonlinear Problems......Page 26
5. A Free Boundary Problem. The Plate Equation......Page 29
6. Second Order Equations......Page 32
7. Higher Order Equations......Page 36
8. Spaces of Continuous Functions. Solution of a Differential Equation......Page 42
9. Boundary Conditions......Page 45
10. Solution of a Boundary Value Problem......Page 59
11. On an Integral Identity......Page 68
12. The Caratheodory Property and the Nemyckii Operators......Page 72
13. Sobolev Spaces......Page 84
14. Differential Operators......Page 93
15. Boundary Value Problems......Page 100
16. Various Generalizations......Page 130
17. Regularity of the Weak Solution......Page 159
18. First Derivative of a Functional......Page 168
19. Potentials of Boundary Value Problems......Page 174
20. The Euler Necessary Condition......Page 178
21. Second Derivative of a Functional......Page 181
22. Lagrange Conditions......Page 183
23. Convex Functionals......Page 186
24. Weak Convergence and Weak Compactness......Page 190
25. Reflexive Spaces......Page 194
26. Existence Theorems......Page 197
27. Minimal Surfaces......Page 217
28. Excursion on Numerical Methods......Page 224
29. Existence Theorems......Page 238
30. The Brouwer and the Leray-Schauder Degree of a Mapping......Page 247
31. General Boundary Conditions for Second Order Ordinary Differential Equations......Page 261
32. Summary of Chapters IV and V. Some Additional Remarks......Page 266
33. Vanishing Nonlinearities. Regular Case......Page 273
34. Vanishing Nonlinearities. Singular Case......Page 280
35. Jumping Nonlinearities with Finite Jumps......Page 289
36. Jumping Nonlinearities with Infinite Jumps......Page 298
37. Rapid Nonlinearities......Page 306
38. Periodic Problems......Page 308
39. Formulation of the Problem......Page 311
40. More on the Definition of the Solution of a Variational Inequality......Page 317
41. Examples......Page 323
42. Some Special Results......Page 337
43. Existence Theorems......Page 342
References......Page 352
Index......Page 356
