On symmetric and periodic solutions of parametric weakly nonlinear ODE with time-reversal symmetries

Time Periodic Solutions for A Pseudo-parabolic Type Equation with Weakly Nonlinear Periodic Sources

In this paper, we prove the existence of nontrivial nonnegative time periodic solutions for a pseudo-parabolic type equation with weakly nonlinear periodic sources. Moreover, we investigate the asymptotic behavior of solutions as the viscous coefficient k tends to zero.

Remark on periodic solutions of nonlinear oscillators

AppIied Mathematics Letters ~w.el~vier.ni/~ocate/~l Abstract-we contribute to the method of trigonometric series for solving differential equations of certain nonlinear oscillators.

EXISTENCE OF PERIODIC SOLUTIONS IN TOTALLY NONLINEAR NEUTRAL DIFFERANCE EQUATIONS WITH VARIABLE DELAY

ON THE PERIODIC SOLUTIONS OF A CLASS OF nTH ORDER NONLINEAR DIFFERENTIAL EQUATIONS *

The nth order differential equation x + c (t )x + ƒ( t,x) = e(t),n>3 is considered. Using the Leray-Schauder principle, it is shown that under certain conditions on the functions involved, this equation possesses a periodic solution.

Computing ODE Symmetries as Abnormal Variational Symmetries

We give a new computational method to obtain symmetries of ordinary differential equations. The proposed approach appears as an extension of a recent algorithm to compute variational symmetries of optimal control problems [Comput. Methods Appl. Math. 5 (2005), no. 4, pp. 387-409], and is based on the resolution of a first order linear PDE that arises as a necessary and sufficient condition of i...