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.