Lojczyk-Krolikiewicz I. A method of appropriate functions to the ordinary second order functional-differential systems / Cracow university of technology. - Krakow: Politechnika Krakowska, 2015. - 134 p. - Bibliogr.: p.133. - ISBN 978-83-72742-847-9 Шифр: (И/В16-L85) 02  Место хранения:   02 | Отделение ГПНТБ СО РАН | Новосибирск

Оглавление / Contents

Preface ......................................................... 7 Chapter I Uniqueness Theorems 1.1. Bounded Solutions §1. Auxiliary Lemmas about quasi-maximum ....................... 10 §2. Inequalities concerning bounded functions .................. 14 §3. Differential-functional inequalities in unbounded interval ................................................... 20 §4. Uniqueness theorems ........................................ 22 §5. Certain applications ....................................... 24 §6. Two examples ............................................... 26 I.2. Unbounded Solutions §7. Linear (a)-Lipschitz condition ............................. 29 §8. A more general boundary condition .......................... 34 §9. A more general (a)-Lipschitz condition ..................... 37 §10.Two examples ............................................... 39 Chapter II Upper and Lower Functions §1. The problem for bounded solutions .......................... 43 §2. The unbounded solutions to the problem posed in 1,1 ........ 48 §3. Some Corollaries ........................................... 51 §4. Boundary condition with β = 0 .............................. 55 Chapter III Existence Theorems 111.1. Bounded Solutions §1. Construction of the auxiliary bounded functions ............ 62 §2. Homogeneous boundary conditions ............................ 67 §3. The nonhomogeneous boundary values problems ................ 71 §4. Boundary value problem with β = 0 .......................... 75 §5. Regularity of vn and wn ..................................... 77 §6. Sequences of appropriate functions to (70) ................. 78 §7. The appropriate functions vn, wn as lower and upper functions .................................................. 82 III.2. Systems of equations §8. Initial information and assumptions ........................ 83 §9. Fundamental lemmas and theorems ............................ 87 §10.The existence theorem of bounded solutions ................. 89 III.3. Unbounded Solutions §11. The indirect method ....................................... 97 §12. The existence theorem concerning the unbounded solutions ................................................ 102 §13. Convergence under a more general Lipschitz condition ..... 108 Chapter IV Complementary knowledge §1. Certain strong coupled systems ............................ 116 §2. Inequalities concerning bounded functions ................. 116 §3. Sets of upper and lower functions ......................... 119 §4. Auxiliary theorems for bounded solutions .................. 122 §5. The existence theorem of bounded solution ................. 124 §6. First order systems of equations .......................... 127 §7. The uniqueness theorem for unbounded solutions ............ 129 §8. The differently set problem ............................... 132 The list of abbreviations ..................................... 132 References .................................................... 133 Streszczenie .................................................. 134