| CHAPTER I | Monotone functions | § 1. Zygmund's lemma
§ 2. A necessary and sufficient condition for a continuous function to be monotone
§ 3. A sufficient condition for a function to be monotone |
| CHAPTER II | Maximum and minimum solution of ordinary differential equationsv | § 4. Some notations and definitions
§ 5. Definition of the maximum (minimum) solution
§ 6. Basic lemmas on strong ordinary differential inequalities
§ 7. Some notions and theorems on ordinary differential equations
§ 8. Local existence of the right-hand maximum solution
§ 9. Global existence of the maximum and minimum solution
§ 10. Continuity of the maximum and minimum solution on the initial point and on the right-hand sides of system |
| CHAPTER III | First order ordinary differential inequalities | § 11. Basic theorems on first order ordinary differential inequalities
§ 12. Necessity of condition V+ (V_) in theorems on differential inequalities
§ 13. Some variants of theorems on differential inequalities
§ 14. Comparison systems
§ 15. Absolute value estimates
§ 16. Infinite systems of ordinary differential inequalities and systems satisfying Carathéodory's conditions |
| CHAPTER IV | Ordinary differential inequalities of higher order and some integral inequalities | § 17. Preliminary remarks and definitions
§ 18. Maximum and minimum solution of an nth order ordinary differential equation
§ 19. Basic theorems on nth order ordinary differential inequalities
§ 20. Comparison equation of order n
§ 21. Absolute value estimates
§ 22. Some integral inequalities |
| CHAPTER V | Cauchy problem for ordinary differential equations | § 23. Estimates of the solution and of its existence interval
§ 24. Estimates of the difference between two solutions
§ 25. Uniqueness criteria
§ 26. Estimates of the error of an approximate solution
§ 27. Stability of the solution
§ 28. Differential inequalities in the complex domain
§ 29. Estimates of the solution and of its radius of convergence for differential equations in the complex domain
§ 30. Estimates of the difference between two solutions in the complex domain
§ 31. Chaplygin method for ordinary differential equations
§ 32. Approximation of solutions of an ordinary differential equation in a Banach space |
| CHAPTER VI | Some auxiliary theorems | § 33. Maximum of a continuous function of n+l variables on n-dimensional planes
§ 34. Maximum of the absolute value of functions of n+1 variables on n-dimensional planes
§ 35. Maximum of a continuous function of several variables on plane sections of a pyramid
§ 36. Comparison systems with right-hand sides depending on parameters |
| CHAPTER VII | Cauchy problem for first order partial differential equations | § 37. Comparison theorems for systems of partial differential inequalities
§ 38. Comparison theorems for overdetermined systems of partial differential inequalities
§ 39. Estimates of the solution
§ 40. Estimate of the existence domain of the solution
§ 41. Estimates of the difference between two solutions
§ 42. Uniqueness criteria
§ 43. Continuous dependence of the solution on initial data and on right-hand sides of system
§ 44. Estimate of the error of an approximate solution
§ 45. Systems with total differentials |
| CHAPTER VIII | Mixed problems for second order partial differential equations of parabolic and hyperbolic type | § 46. Ellipticity and parabolicity
§ 47. Mixed problems
§ 48. Estimates of the solution of the first mixed problem
§ 49. Estimates of the difference between two solutions of the first mixed problem
§ 50. Uniqueness criteria for the solution of the first mixed problem
§ 51. Continuous dependence of the solution of the first mixed problem on initial and boundary values and on the right-hand sides of system
§ 52. Stability of the solution of the first mixed problem
§ 53. Preliminary remarks and lemmas referring to the second mixed problem
§ 54. Sufficient conditions for the existence of sign-stabilizing factors
§ 55. Analogues of theorems in § 48-52 in case of the second mixed problem
§ 56. Energy estimates for solutions of hyperbolic equations |
| CHAPTER IX | Partial differential inequalities of first order | § 57. Systems of strong first order partial differential inequalities
§ 58. Overdetermined systems of strong first order partial differential inequalities
§ 59. Systems of weak first order partial differential inequalities
§ 60. Overdetermined systems of weak first order partial differential inequalities
§ 61. Comparison systems of first order partial differential equations
§ 62. Estimates of solutions of first order partial differential equations and a uniqueness criterion |
| CHAPTER X | Second order partial differential inequalities of parabolic type | § 63. Strong partial differential inequalities of parabolic type
§ 64. Weak partial differential inequalities of parabolic type
§ 65. Parabolic differential inequalities in unbounded regions
§ 66. The Chaplygin method for parabolic equations
§ 67. Maximum solution of the parabolic equation |
| CHAPTER XI | Differential inequalities in linear spaces | § 68. Convex sets in linear topological spaces
§ 69. Mean value theorems
§ 70. Strong differential inequalities
§ 71. Bendixson equation and differential inequalities
§ 72. Linear differential inequalities in Banach spaces I
§ 73. Linear differential inequalities in Banach. spaces II
§ 74. Almost linear differential inequalities in Banach spaces |
| Materiały redakcyjne | | References, list of special symbols, index, contents |
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