Twist Character of the Fourth Order Resonant Periodic 1 Solution 2
نویسندگان
چکیده
In this paper, we will give, for the periodic solution of the scalar Newtonian 5 equation, some twist criteria which can deal with the fourth order resonant 6 case. These are established by developing some new estimates for the periodic 7 solution of the Ermakov–Pinney equation, for which the associated Hill equa8 tion may across the fourth order resonances. As a concrete example, the least 9 amplitude periodic solution of the forced pendulum is proved to be twist 10 even when the frequency acroses the fourth order resonances. This improves 11 the results in Lei et al. (2003). Twist character of the least amplitude peri12 odic solution of the forced pendulm. SIAM J. Math. Anal. 35, 844–867. 13
منابع مشابه
Twist Character of the Least Amplitude Periodic Solution of the Forced Pendulum
In this paper, we will derive some twist criteria for the periodic solution of a periodic scalar Newtonian equation using the third order approximation. As an application to the forced pendulum ẍ + ω2 sinx = p(t), we will find an explicit bound P (ω) for the L1 norm, ‖p‖1, of the periodic forcing p(t) using the frequency ω as a parameter such that the least amplitude periodic solution of the fo...
متن کاملPeriodic solutions of fourth-order delay differential equation
In this paper the periodic solutions of fourth order delay differential equation of the form $ddddot{x}(t)+adddot{x}(t)+f(ddot{x}(t-tau(t)))+g(dot{x}(t-tau(t)))+h({x}(t-tau(t)))=p(t)$ is investigated. Some new positive periodic criteria are given.
متن کامل(Vanishing) Twist in the Saddle-Centre and Period-Doubling Bifurcation
The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1 : 1 (saddle-centre) and 1 : 2 (period-doubling). The twist, which is the derivative of the rotation number with respect to the action, is studied near these bifurcations. When the twist vanishes the nondegeneracy condition of the (isoenergetic) KAM theorem is not...
متن کاملPeriodic Solutions for Some Fully Nonlinear Fourth Order Differential Equations
In this paper we present sufficient conditions for the existence of solutions to the periodic fourth order boundary value problem u(x) = f(x, u(x), u′(x), u′′(x), u′′′(x)) u(a) = u(b), i = 0, 1, 2, 3, for x ∈ [a, b], and f : [a, b] × R4 → R a continuous function. To the best of our knowledge it is the first time where this type of general nonlinearities is considered in fourth order equations w...
متن کاملMathematical modeling of optimized SIRS epidemic model and some dynamical behavior of the solution
In this paper, a generalized mathematical model of spread of infectious disease as SIRS epidemic model is considered as a nonlinear system of differential equation. We prove that for positive initial conditions the resulting equivalence system has positive solution and under some hypothesis, this system with initial positive condition, has a positive $T$-periodic solution which is globally asym...
متن کامل