Electronic Journal of Differential Equations,
Conference 05 (2000), pp. 69-80.

Title:  Center manifold and exponentially-bounded solutions 
  of a forced Newtonian system with dissipation.

Authors: Luis Garcia (Univ. de los Andes, Merida, Venezuela) 
  Hugo Leiva (Univ. de los Andes, Merida, Venezuela) 
 
Abstract: 
  We study the existence of exponentially-bounded solutions to
  the following system of second-order ordinary differential equations with 
  dissipation:  
  $$
  u''+cu'+Au+kH(u) = P(t), \quad u \in {\mathbb R}^n, \quad t \in {\mathbb R},
  $$
  where $c$ and $k$ are positive constants, $H$ is a globally Lipschitz 
  function, and $P$ is a bounded and continuous function. 
  $A$ is a $n \times n$ symmetric matrix whose first eigenvalue 
  is equal to zero and the others are positive.
  Under these conditions, we prove that for some values of $c$, 
  and $k$ there exist a continuous manifold such that solutions starting 
  in this manifold are exponentially bounded.  
  Our results are applied to the spatial discretization of well-known 
  second-order partial differential equations with Neumann boundary 
  conditions. 

Published October 24, 2000.
Math Subject Classifications: 34A34, 34C27, 34C30.
Key Words: center manifold; exponentially-bounded solutions.