## Abstract We prove, by variational arguments, the existence of a solution to the boundary value problem in the half line equation image where __c__ β₯ 0 and __a__ belongs to a certain class of positive functions. The existence of such a solution in the case __c__ = 0 means that the system (0.1)
Some conditions for a center of autonomous and nonautonomous systems
β Scribed by M.A.M. Alwash
- Publisher
- Elsevier Science
- Year
- 1993
- Tongue
- English
- Weight
- 351 KB
- Volume
- 6
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
β¦ Synopsis
We give some conditions which imply that the origin is a center for polynomial twodimensional systems. A related cubic nonautonomous equation is also considered.
π SIMILAR VOLUMES
In this work, we study necessary and sufficient conditions for the existence of centers in two families of linear centers with homogeneous quartic and quintic nonlinearities. Systems of this class are called Kukles homogeneous systems. Systems of this type were studied, for the first time. by Kukles
The two-parameter perturbation method, applied to the example of periodic oscillations in periodically driven mmlinear dynamical systems, is presented. The analytical conditions are given for the existence of a two-parameter family of periodic orbits in nonautonomous dynamical systems in both non-re
In this article, we give a necessary condition for the existence of periodic solutions of certain three dimensional autonomous systems. This may become useful in further investigations. Our claims are proved and supported by certain examples for the third order autonomous systems.