Author | Bartuลกek, Miroslav. author |
---|---|
Title | The Nonlinear Limit-Point/Limit-Circle Problem [electronic resource] / by Miroslav Bartuลกek, Zuzana Doลกlรก, John R. Graef |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8218-7 |
Descript | IX, 162 p. online resource |
1 Origins of the Limit-Point/Limit-Circle Problem -- 1.1 The Weyl Alternative -- 1.2 The Deficiency Index Problem -- 1.3 Second Order Linear Equations -- 2 Basic Definitions -- 2.1 Description of the Limit-Point/Limit-Circle Problem -- 2.2 Continuable and Singular Solutions -- 2.3 Extension of the LP/LC Properties to Singular Solutions -- 3 Second Order Nonlinear Equations -- 3.1 Introduction -- 3.2 The Superlinear Equation -- 3.3 The Sublinear Equation -- 3.4 Equations with r(t) ? 0 -- 4 Some Early Limit-Point and Limit-Circle Results -- 4.1 Wintnerโs Result -- 4.2 Early Results on Higher Order Linear Equations -- 4.3 Nonlinear Limit-Point Results for Second Order Equations -- 4.4 Nonlinear Limit-Point Results for Higher Order Equations -- 4.5 Some New Generalizations of the Early Results -- 5 Relationship to Other Asymptotic Properties -- 5.1 Second Order Linear Equations -- 5.2 Second Order Nonlinear Equations -- 6 Third Order Differential Equations -- 6.1 Equations with Quasiderivatives -- 6.2 Linear Equations -- 6.3 Nonlinear Three-Term Equations -- 7 Fourth Order Differential Equations -- 7.1 Equations with Quasiderivatives -- 7.2 Sublinear Equations in Self-Adjoint Form -- 7.3 Two-Term Equations -- 7.4 Linear Equations -- 8 Nonlinear Differential Equations of n-th Order -- 8.1 Introduction -- 8.2 Basic Lemmas -- 8.3 Limit-Point Results -- 9 Relationship to Spectral Theory -- 9.1 Introduction -- 9.2 Self-Adjoint Linear Fourth Order Equations -- 9.3 Two-Term Even Order Linear Equations -- Author Index