Asymptotic Solutions of Strongly Nonlinear Systems of Differential Equations

• Main Authors: Kozlov, Valery V. (Author), Furta, Stanislav D. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2013.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Differentiable dynamical systems.; Differential Equations.; Mathematical physics.; Ordinary Differential Equations.; Dynamical Systems and Ergodic Theory.; Mathematical Methods in Physics.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-3-642-33817-5

The book is dedicated to the construction of particular solutions of systems of ordinary differential equations in the form of series that are analogous to those used in Lyapunovs first method. A prominent place is given to asymptotic solutions that tend to an equilibrium position, especially in th...

Table of Contents:

• Preface
• Semi-quasihomogeneous systems of ordinary differential equations
• 2. The critical case of purely imaginary kernels
• 3. Singular problems
• 4. The inverse problem for the Lagrange theorem on the stability of equilibrium and other related problems
• Appendix A. Nonexponential asymptotic solutions of systems of functional-differential equations
• Appendix B. Arithmetic properties of the eigenvalues of the Kovalevsky matrix and conditions for the nonintegrability of semi-quasihomogeneous systems of ordinary dierential equations
• Bibliography.