Remarks on Forced Equations of the Double Pendulum Type

Subharmonic Oscillations of Forced Pendulum-Type Equations

where f is periodic with minimal period T and mean value zero. We have in mind as a particular case the pendulum equation, where g(x) = A sin x. First results on the existence of subharmonic orbits in a neighborhood of a given periodic motion were obtained by Birkhoff and Lewis (cf. [3] and [ 143) by perturbation-type techniques. Rabinowitz [ 151 was able to prove the existence of subharmonic s...

Degenerate Equations of Pendulum-type

the investigation of the relationship between type a and type b personalities and quality of translation

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Remarks on the Mass Constraint for KP-Type Equations

For a rather general class of equations of Kadomtsev-Petviashvili (KP) type, we prove that the zero-mass (in x) constraint is satisfied at any non zero time even if it is not satisfied at initial time zero. Our results are based on a precise analysis of the fundamental solution of the linear part and its anti x-derivative.

Convergence of periodically forced rank-type equations

Consider a difference equation which takes the k-th largest output of m functions of the previousm terms of the sequence. If the functions are also allowed to change periodically as the difference equation evolves, this is analogous to a differential equation with periodic forcing. A large class of such non-autonomous difference equations are shown to converge to a periodic limit, which is inde...