Ordinary differential equations and boundary value problems: Volume 2 Boundary value problems
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New Jersey
World Scientific
[2019]
|
| Series: | Trends in abstract and applied analysis
volume 8 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | xii, 330 Seiten Diagramme |
| ISBN: | 9789813274020 |
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MARC
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| 245 | 1 | 0 | |a Ordinary differential equations and boundary value problems |n Volume 2 |p Boundary value problems |c John R. Graef, Johnny Henderson, Lingju Kong, Xueyan Sherry Liu |
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Record in the Search Index
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| adam_text | Contents Preface 1. vii Introduction to Boundary Value Problems 1.1 1.2 1.3 Introduction.............................................................. Disconjugacy............................. Disconjugacy for Equations of Arbitrary Order............... 1 1 2 18 Bibliography 23 2. Linear Problems and Green’s Functions 25 2.1 2.2 2.3 2.4 25 31 33 35 Introduction to Linear ODE’s................................... Linear BVP’s........................................................................ Green’s Functions for Linear BVP’s.................................... Properties of the Green’s Function.................................... 2.4.1 Second method for constructing the Green’s function............................................ 2.4.2 Another approach using the properties............... 2.4.3 Green’s functions for general linear homogeneous BVP’s............ ...................................... 36 37 40 Bibliography 47 3. 49 Existence of Solutions I 3.1 3.2 Local Existence Theorems for Solutions of BVP’s for the Nonlinear Equation, y = ƒ(x, y,y ) Linear Second Order Inequalities ........................ ІХ 49 63
Volume 2: Boundary Value Problems x 3.3 3.4 Existence of Solutions of BVP’sfor Nonlinear ODE’s ... Existence of Solutions of BVP’s for Nonlinear Higher Order ODE’s.................................................................................... 75 89 Bibliography 105 4. 107 Existence of Solutions II 4.1 4.2 Existence of Solutions of BVP’s Associated with y = f{x,y,y’,y ) A Converse of Lemma 4.3.......................................... 107 127 Bibliography 133 5. 135 Solution Matching 5.1 5.2 Introduction . . ....................................................................... 5.1.1 Uniqueness and existence of solutions bymatching ............................................ 5.1.2 Uniqueness and existence of solutions for a larger class of BVP’s by matching.................................... Five-Point Nonlocal BVP’s for nth Order ODE’s by Solution Matching........................................................ 5.2.1 Uniqueness of solutions.......................... 5.2.2 Existence of solutions ............................................. 135 136 140 141 142 144 Bibliography 147 6. 149 Comparison of Smallest Eigenvalues 6.1 6.2 6.3 Comparison Theorems for 2-Point Conjugate Eigenvalue Problems............................................................ Eigenvalue Comparisons for Nonlocal BVP’s..................... Solutions of Second Order Multi-Point BVP’s....... 6.3.1 Preliminary lemmas................................................ 6.3.2 Existence results . .................................... 149 156 160 161 168 Bibliography 185 7. 187 BVP’s for Functional
Differential Equations 7.1 Existence of Solutions for BVP’s for Second Order Functional Differential Equations....................................... 187
Contents 7.2 7.3 xi Periodic Solutions for First Order Functional Differential Equations.... .......... ............................................................. 193 Periodic Solutions for Functional Differential Equations with Sign-Changing Nonlinearities.......................... 199 7.3.1 Preliminary results ................................................ 200 7.3.2 Existence results............................................... .. . 208 7.3.3 Proofs of the existence results .............................. 211 Bibliography 219 8. 221 Positive Solutions 8.1 8.2 8.3 8.4 8.5 8.6 Positive Solutions for Nonlinear Eigenvalue Problems . . . 221 8.1.1 Solutions in the cone ............................................. 222 Multiplicity of Positive Solutions................................ 226 Positive Solutions for Nonlinear Difference Equations . . . 230 Multiple Symmetric Positive Solutions.............................. 237 Positive Solutions for a Singular Third Order BVP .... 241 8.5.1 A priori bounds on norms of solutions ....... 245 8.5.2 Existence of positive solutions............ ..................... 247 Positive Solutions for Third Order BVP’s with p-Laplacian............................................... 249 8.6.1 Main results . . ...................................................... 250 8.6.2 Proofs of the main results . .................................... 252 Bibliography 267 9. 271 Boundary Data Smoothness 9.1 Differentiation of Solutions with Respect to Boundary Con ditions ....................................................................................
271 Bibliography 281 10. Nodal Solutions of BVP’s for ODE’s 283 10.1 Nodal 10.1.1 10.1.2 10.2 Nodal 10.2.1 10.2.2 10.3 Nodal Solutions of Nonlinear BVP’s with Separated BC’s 283 Main results............................................................ 284 Proofs of the main results....................................... 287 Solutions of Nonlocal BVP’s — I........................... 302 Main results............................................................ 303 Proofs of the main results . . ................................. 307 Solutions of Nonlocal BVP’s — II . .·.....................311
Volume 2: Boundary Value Problems xii 10.3.1 Existence and nonexistence of nodal solutions 10.3.2 Dependence of nodal solutions on the problem 313 319 Bibliography 327 Index 329
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| author | Graef, John R. 1942- Henderson, Johnny Kong, Lingju |
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| id | DE-604.BV045273104 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T08:13:32Z |
| institution | BVB |
| isbn | 9789813274020 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030660826 |
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| physical | xii, 330 Seiten Diagramme |
| publishDate | 2019 |
| publishDateSearch | 2019 |
| publishDateSort | 2019 |
| publisher | World Scientific |
| record_format | marc |
| series | Trends in abstract and applied analysis |
| series2 | Trends in abstract and applied analysis |
| spelling | Graef, John R. 1942- Verfasser (DE-588)140965459 aut Ordinary differential equations and boundary value problems Volume 2 Boundary value problems John R. Graef, Johnny Henderson, Lingju Kong, Xueyan Sherry Liu New Jersey World Scientific [2019] xii, 330 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Trends in abstract and applied analysis volume 8 Trends in abstract and applied analysis Henderson, Johnny Verfasser (DE-588)170788350 aut Kong, Lingju Verfasser (DE-588)1080395563 aut (DE-604)BV044931532 2 Trends in abstract and applied analysis volume 8 (DE-604)BV043530503 8 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030660826&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Graef, John R. 1942- Henderson, Johnny Kong, Lingju Ordinary differential equations and boundary value problems Trends in abstract and applied analysis |
| title | Ordinary differential equations and boundary value problems |
| title_auth | Ordinary differential equations and boundary value problems |
| title_exact_search | Ordinary differential equations and boundary value problems |
| title_full | Ordinary differential equations and boundary value problems Volume 2 Boundary value problems John R. Graef, Johnny Henderson, Lingju Kong, Xueyan Sherry Liu |
| title_fullStr | Ordinary differential equations and boundary value problems Volume 2 Boundary value problems John R. Graef, Johnny Henderson, Lingju Kong, Xueyan Sherry Liu |
| title_full_unstemmed | Ordinary differential equations and boundary value problems Volume 2 Boundary value problems John R. Graef, Johnny Henderson, Lingju Kong, Xueyan Sherry Liu |
| title_short | Ordinary differential equations and boundary value problems |
| title_sort | ordinary differential equations and boundary value problems boundary value problems |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030660826&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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