Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 69-80.

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

Luis Garcia & Hugo Leiva

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.

Show me the PDF file (141K), TEX file, and other files for this article.

Luis Garcia
Universidad de los Andes
Facultad de Ciencias
Departamento de Matematica
Merida 5101-Venezuela
Hugo Leiva
Universidad de los Andes
Facultad de Ciencias
Departamento de Matematica
Merida 5101-Venezuela
e-mail: hleiva@ula.ve

Return to the EJDE web page