Periodic solutions in n dimensions and Volterra equations |
| |
Authors: | Jane Cronin |
| |
Institution: | Department of Mathematics, Rutgers University, New Brunswick, New Jersey 08903 USA |
| |
Abstract: | If a nonlinear autonomous n-dimensional system of ordinary differential equations has a bounded solution with a certain uniform stability property, this solution approaches an almost periodic solution with the same stability property. (More precisely, the almost periodic solution is in the set of ω-limit points of the given solution.) If the bounded solution has, in addition to the uniform stability property, an asymptotic stability property, then the solution approaches a periodic solution with the same stability properties. Practical (i.e., computable) sufficient conditions for boundedness of solutions are obtained. The results are applied to generalized Volterra equations. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|