Jose Luiz Boldrini & Janete Crema
Abstract:
We study the existence of periodic solutions for a class of
quasi-parabolic equations involving the p-Laplacian (or any other
nonlinear operators of similar class) perturbed by nonlinear terms and
forced by rather irregular periodic in time excitations (including what
we call abrupt changes). These equations may model problems for which,
aside from the presence of the kind of nonlinear dissipation associated
to the p-Laplacian, other nonlinear and not necessarily dissipative
mechanisms occur. We look for boundedness conditions on these periodic
excitations and nonlinear perturbations sufficient to guarantee the
existence of periodic responses (solutions) of the same period.
Submitted March 11, 1998. Published May 30, 1998.
Math Subject Classification: 35K55, 35B10.
Key Words: quasi-parabolic equations, periodic solutions, p-Laplacian
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Jose Luiz Boldrini
UNICAMP-IMECC; CP 6065; 13081-980 Campinas, SP, Brazil.
e-mail: boldrini@ime.unicamp.br
Janete Crema
USP - ICMSC; CP 668, 13560-970 S\~ao Carlos, SP, Brazil