Asymptotic behavior for differential equations which cannot be locally linearized |
| |
Authors: | A Lasota Aaron Strauss |
| |
Institution: | Department of Mathematics, University of Maryland, College Park, Maryland 20742 USA |
| |
Abstract: | For functions ? which are continuous and locally Lipschitz the authors define a multi-valued differential Df and prove that if all solutions of the multi-valued differential equation u′ ? Df(u) approach zero as t → ∞, then all solutions x(·) of x′ = ?(x) with small |x(0)| approach zero exponentially as t → ∞. If ? is continuously differentiable, then Df coincides with the (single-valued) Frechet differential of ?. Other results on the asymptotic behavior of solutions of perturbed, multi-valued differential equations are presented. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|