Nonlinear Differential Equations,
Electron. J. Diff. Eqns., Conf. 05, 2000, pp. 6980.
Center manifold and exponentiallybounded solutions
of a forced Newtonian system with dissipation
Luis Garcia & Hugo Leiva
Abstract:
We study the existence of exponentiallybounded solutions to
the following system of secondorder ordinary differential equations with
dissipation:
where
and
are positive constants,
is a globally Lipschitz function, and
is a bounded and continuous function.
is a
symmetric matrix whose first eigenvalue
is equal to zero and the others are positive.
Under these conditions, we prove that for some values of
,
and
there exist a continuous manifold such that solutions starting
in this manifold are exponentially bounded.
Our results are applied to the spatial discretization of wellknown
secondorder partial differential equations with Neumann boundary
conditions.
Published October 24, 2000.
Math Subject Classifications: 34A34, 34C27, 34C30.
Key Words: center manifold, exponentiallybounded solutions.
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Luis Garcia
Universidad de los Andes
Facultad de Ciencias
Departamento de Matematica
Merida 5101Venezuela 

Hugo Leiva
Universidad de los Andes
Facultad de Ciencias
Departamento de Matematica
Merida 5101Venezuela
email: hleiva@ula.ve 
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