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v. 1 ISBN 9780444511287
内容説明
The book contains seven survey papers about ordinary differential equations.
The common feature of all papers consists in the fact that nonlinear equations are focused on. This reflects the situation in modern mathematical modelling - nonlinear mathematical models are more realistic and describe the real world problems more accurately. The implications are that new methods and approaches have to be looked for, developed and adopted in order to understand and solve nonlinear ordinary differential equations.
The purpose of this volume is to inform the mathematical community and also other scientists interested in and using the mathematical apparatus of ordinary differential equations, about some of these methods and possible applications.
目次
1. A Survey of Recent Results for Initial and Boundary Value Problems Singular in the Dependent Variable (R. Agarwal, D. O'Regan).2. The Lower and Upper Solutions Method for Boundary Value Problems (C. De Coster, P. Habets).3. Half-Linear Differential Equations (O. Doysl'y).4. Radial Solutions of Quasilinear Elliptic Differential Equations (J. Jacobsen and K. Schmitt).5. Integrability of Polynomial Differential Systems (J. Llibre).6. Global Results for the Forced Pendulum Equation (J. Mawhin).7. Wazewski Method and Conley Index (R. Srzednicki).
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v. 2 ISBN 9780444520272
内容説明
This handbook is the second volume in a series devoted to self contained and up-to-date surveys in the theory of ordinary differential equations, writtenby leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields, in order to make the chapters of the volume accessible to a wide audience.
目次
1. Optimal Control of Ordinary Differential Equations, (V. Barbu, C. Lefter). 2. Hamiltonian Systems: Periodic and Homoclinic Solutions by Variational Methods, (T. Bartsch, A. Szulkin) . 3. Differential Equations on Closed Sets (O. Carja, I.I. Vrabie) . 4. Monotone Dynamical Systems (M.W. Hirsch, H. Smith) . 5. Planar Periodic Systems of Population Dynamics (J. Lopez-Gomez) . 6. Nonlocal Initial and Boundary Value Problems: a survey (S.K. Ntouyas).
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v. 3 ISBN 9780444528490
内容説明
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience.
These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume.
目次
1. Topological Principles for Ordinary Differential Equations (J. Andres)
2. Heteroclinic Orbtis for Some Classes of Second and Fourth Order Differential Equations (D.Bonheure and L. Sanchez)
3. A Qualitative Analysis, via Lower and Upper Solutions, of First Order Periodic Evolutionary Equations with Lack of Uniqueness (C. DeCoster, F. Obersnel and P. Omari)
4. Bifurcation Theory of Limit Cycles of Planar Systems (M. Han)
5. Functional Differential Equations with State-Dependent Delays: Theory and Applications (F. Hartung, T. Krisztin, H.O. Walther and J. Wu)
6. Global Solutions Branches and Exact Multiplicity of Solutions for Two Point Boundary Value Problems (P. Korman)
7. Singularities and Laplacians in Boundary Value Problems for Nonlinear Ordinary Differential Equations (I. Rachunkova, S. Stanek and M. Tvrdy)
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v. 4 ISBN 9780444530318
内容説明
This handbook is the fourth volume in a series of volumes devoted to self-contained and up-to-date surveys in the theory of ordinary differential equations, with an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wider audience.
目次
Chapter 1: Symmetric Hopf Bifurcation: Twisted Degree Approach
Chapter 2: Nonautonomous Differential Systems in Two Dimensions
Chapter 3: Complex Differential Equations
Chapter 4: Transversal Periodic-to-Periodic Homoclinic Orbits
Chapter 5: Successive Approximation Techniques in Non-Linear Boundary Value Problems for Ordinary Differential Equations
Chapter 6: Analytic Ordinary Differential Equations and Their Local Classification
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