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E-raamat: Strong Nonlinear Limit-point/limit-circle Problem, The

(Univ Of Tennessee At Chattanooga, Usa), (Masaryk Univ, Czech Republic)
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Strong Nonlinear Limit-point/limit-circle Problem, TheSuurem pilt
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This graduate textbook explains some of the early results on limit-point and limit-circle results for linear equations, such as those of Wintner, and various attempts at extensions to nonlinear equations by Atkinson, Burlak, Detki, Hallam, and Suyemoto and Waltman. After introducing the strong limit-point and strong limit-circle properties of solutions, the authors consider second-order equations with damping terms, higher order equations, second-order delay differential equations, and the use of transformations in obtaining nonlinear solutions. The last chapter presents open problems and directions for future research. Annotation ©2018 Ringgold, Inc., Portland, OR (protoview.com)
Preface vii
1 The Origins of the Limit-Point/Limit-Circle Problem
1(4)
1.1 Introduction
1(1)
1.2 The Weyl Alternative
1(4)
2 Equations with p-Laplacian
5(34)
2.1 Introduction
5(1)
2.2 Second-Order Unforced Equations
5(2)
2.3 Preliminary Lemmas
7(10)
2.4 Nonlinear Limit-Point/Limit-Circle Results
17(4)
2.5 The Forced Equation
21(6)
2.6 Asymptotic Properties of Solutions of the Forced Equation
27(9)
2.7 Examples and Discussion
36(3)
3 Strong Limit-Point/Limit-Circle Properties
39(106)
3.1 Introduction
39(1)
3.2 The Strong Limit-Point Property
39(3)
3.3 Some Lemmas
42(8)
3.4 Strong Nonlinear Limit-Point Results for Emden-Fowler Equations
50(6)
3.5 Sub-Half-Linear and Super-Half-Linear Equations
56(3)
3.6 Preliminary Lemmas
59(11)
3.7 Strong Nonlinear Limit-Point/Limit-Circle Results for Sub-Half-Linear Equations
70(4)
3.8 Strong Nonlinear Limit-Point/Limit-Circle Results for Super-Half-Linear Equations
74(6)
3.9 The Forced Equation
80(24)
3.10 Further Results for the Unforced Equation
104(5)
3.11 Equations with ∫∞0 (a-1/p(t) + r(t))dt < ∞
109(14)
3.12 Thomas--Fermi Equations
123(2)
3.13 Classification of Solutions
125(8)
3.14 Limit-Point/Limit-Circle Solutions of Thomas-Fermi Type Equations
133(4)
3.15 Examples and Further Discussion
137(8)
4 Damped Equations
145(34)
4.1 Introduction
145(1)
4.2 Notation
146(2)
4.3 The Sub-Half-Linear Case: Preliminary Lemmas
148(9)
4.4 The Sub-Half-Linear Case: Main Results
157(2)
4.5 The Super-Half-Linear Case: Preliminary Lemmas
159(10)
4.6 The Super-Half-Linear Case: Main Results
169(2)
4.7 The Case p = q
171(3)
4.8 Examples and Discussion
174(5)
5 Higher Order Equations
179(32)
5.1 Introduction
179(1)
5.2 Equations of Order 2n
179(9)
5.3 Limit-Point/Limit-Circle Solutions of Even-Order Equations
188(8)
5.4 Fourth-Order Equations
196(8)
5.5 Limit-Point/Limit-Circle and Related Properties of Solutions of Fourth-Order Equations
204(7)
6 Delay Equations I
211(34)
6.1 Introduction
211(1)
6.2 Limit-Point/Limit-Circle and Other Properties of Solutions
211(3)
6.3 Preliminary Lemmas
214(9)
6.4 Nonoscillatory Solutions
223(8)
6.5 Oscillatory Solutions
231(11)
6.6 Examples
242(3)
7 Delay Equations II
245(32)
7.1 Introduction
245(1)
7.2 Preliminaries
246(15)
7.3 Behavior of Nonoscillatory Solutions
261(5)
7.4 Behavior of Oscillatory Solutions
266(5)
7.5 Limit-Point/Limit-Circle Properties of Solutions
271(4)
7.6 Examples
275(2)
8 Transformations of the Basic Equation
277(16)
8.1 Introduction
277(2)
8.2 Preliminaries
279(6)
8.3 Limit-Point and Limit-Circle Results
285(5)
8.4 Examples and Discussion
290(3)
9 Notes, Open Problems, and Future Directions
293(6)
9.1 Introduction
293(1)
9.2 Notes and Open Problems
293(3)
9.3 Directions for Future Research
296(3)
Bibliography 299(12)
Index 311
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