Under conditions of Levinson-Smith type, we prove the existence of a τ -periodic solution for the perturbed generalized Liénard equation u′′ + φ(u, u′)u′ + ψ(u) = ω( t τ , u, u′) with periodic forcing term. Also we deduce sufficient condition for existence of a periodic solution for the equation

Based on symbolic manipulation program Maple and using Riccati equation mapping method several explicit exact solutions including kink, soliton-like, periodic and rational solutions are obtained for (2+1)-dimensional variable coefficient Broer-Kaup system in quite a straightforward manner. The known solutions of Riccati equation are used to construct new solutions for variable coefficient Broer...

We studied the amplification of the solution of a Mathieu-like equation with multiplicative white noise. This equation has a periodic varying mass term. The exponents were calculated numerically by solving the stochastic differential equations by symplectic method. It was shown that the exponent increases with a parameter α in the range of large α, where the value of α is determined by the inte...

Recommended by Jianshe Yu The permanence and the existence of periodic solution for a discrete nonautonomous competitive system with multidelays are considered. Also the stability of the periodic solution is discussed. Numerical examples are given to confirm the theoretical results.

We study the evolution of the one dimensional periodic cubic Schrödinger equation (NLS) with bounded variation data. For the linear evolution, it is known that for irrational times the solution is a continuous, nowhere differentiable fractal-like curve. For rational times the solution is a linear combination of finitely many translates of the initial data. Such a dichotomy was fist observed by ...

Coexistence The special case when all the independent solutions of a linear, T -periodic ODE are T -periodic. Hill’s equation A second order ODE of the form ẍ + p(t)x = 0, with p(t) T -periodic. Instability pockets Finite domains, usually intersections of instability tongues, where the trivial solution of linear, T -periodic ODEs is unstable. Instability tongues Domains in parameter space where...

This paper deals with the homogenization of a quasilinear elliptic problem having singular lower order term and posed in two-component domain an ε-periodic imperfect interface. We prescribe Dirichlet condition on exterior boundary, while we assume that continuous heat flux is proportional to jump solution interface via function ε γ . prove result for − 1 < by means periodic unfolding method ...