Regularity of Time-Periodic Solutions to Autonomous Semilinear Hyperbolic PDEs

Homogenization of periodic semilinear parabolic degenerate PDEs

In this paper a second order semilinear parabolic PDE with rapidly oscillating coefficients is homogenized. The novelty of our result lies in the fact that we allow the second order part of the differential operator to be degenerate in some part of Rd . Our fully probabilistic method is based on the deep connection between PDEs and BSDEs and the weak convergence of a class of diffusion processe...

PERIODIC SOLUTIONS OF CERTAIN THREE DIMENSIONAL AUTONOMOUS SYSTEMS

There has been extensive work on the existence of periodic solutions for nonlinear second order autonomous differantial equations, but little work regarding the third order problems. The popular Poincare-Bendixon theorem applies well to the former but not the latter (see [2] and [3]). We give a necessary condition for the existence of periodic solutions for the third order autonomous system...

[hal-00359844, v1] Homogenization of periodic semilinear parabolic degenerate PDEs

(a) LERSTAD, UFR S.A.T, Université Gaston Berger, BP 234, Saint-Louis, SENEGAL. email : [email protected] (b) CEREMADE, Université Paris-Dauphine, Place du maréchal De Lattre de Tassigny, 75775 Paris cedex 16, FRANCE. email : [email protected] (c) CMI, LATP-UMR 6632, Université de Provence, 39 rue F. Joliot Curie, 13453 Marseille cedex 13, FRANCE. email : [email protected] Abstr...

Families of Periodic Solutions of Resonant PDEs

Periodic Solutions of Semilinear Impulsive Periodic System with Time-Varying Generating Operators on Banach Space

A class of semilinear impulsive periodic systems with time-varying generating operators on Banach space is considered. Using impulsive periodic evolution operator given by us, the T0periodic PC-mild solution is introduced and suitable Poincaré operator is constructed. Showing the compactness of Poincaré operator and using a new generalized Gronwall inequality with mixed type integral operators ...