Periodic solutions to second order nonautonomous differential systems with unbounded nonlinearities
β Scribed by Zhiqing Han
- Publisher
- John Wiley and Sons
- Year
- 2011
- Tongue
- English
- Weight
- 111 KB
- Volume
- 284
- Category
- Article
- ISSN
- 0025-584X
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π SIMILAR VOLUMES
The equation xΠ t q x t s bx t y 1 , where ΠΈ designates the greatest integer function, can be described in brief by two amazing properties. First, for certain values of the coefficients, some or all of its solutions are monotone although the corresponding homogeneous equation is clearly oscillatory.
We consider the second-order gradient-like system where F : R N Γ R is analytic and g: R N Γ R N is Lipschitz and coercive with g(0)=0. We prove the convergence of global and bounded solutions of (1) to some equilibrium points.
## Abstract In this paper, we employ a wellβknown fixed point theorem for cones to study the existence of positive periodic solutions to the __n__ βdimensional system __x__ β³ + __A__ (__t__)__x__ = __H__ (__t__)__G__ (__x__). Moreover, the eigenvalue intervals for __x__ β³ + __A__ (__t__)__x__ = __Ξ»
The existence and multiplicity of periodic solutions are obtained for the nonau-Ε½ . tonomous second order systems with locally coercive potential; that is, F t, x Βͺ < < w x qΟ± as x Βͺ Ο± for a.e. t in some positive-measure subset of 0, T , by using an analogy of Egorov's Theorem, the properties of sub