A homotopy index continuation method and periodic solutions of second-order gradient systems
β Scribed by Krzysztof P Rybakowski
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 746 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0022-0396
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π SIMILAR VOLUMES
Some existence theorems are obtained by the least action principle for periodic solutions of nonautonomous second-order systems with a potential which is the sum of a subconvex function and a subquadratic function.
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»