Even and periodic solutions of the equation ü + g(u) = e(t)

Even periodic solutions of higher order duffing differential equations

“…Although there are a number of other studies which are related to even and periodic solutions (see e.g. [1]- [7]), this number is insignificant when compared with the large number of studies related to general periodic solutions.…”

“…In [1], even and periodic solutions are found for the Duffing equation (1) x (t) + g(x(t)) = p(t), where g and p are real continuous functions defined on , g is Lipschitz, p is periodic with minimum period 2π and even, that is, p(−t) = p(t) for t ∈ . A typical example of such an equation is x + x 3 = 0.04 cos t, which has been studied and many of its even and periodic solutions are observed numerically.…”

“…As mentioned in [1], the study of existence of periodic solutions of (1) is usually reduced to the one of existence of fixed points of the Poincaré mapping, and in the case of even and periodic solutions, it is reduced to the one of a simple boundary value problem in the phase plane. In our case, the concept of boundary value problem is still useful but since we are dealing with higher order equations, we find the phase plane analysis difficult.…”

The periodic motions of a class of symmetric superlinear Hill’s impact equations

“…有关非线性 Hill 方程相关的最新成果可 参见文献 [10][11][12][13][14][15]. 当 q(t) ≡ 1 时, 方程 (1.1) 是有名的 Duffing 方程, 关于 Duffing 方程周期解的研究已经有了许多 结果 [16][17][18] . Nakajima [18] 在超线性条件…”

“…当 q(t) ≡ 1 时, 方程 (1.1) 是有名的 Duffing 方程, 关于 Duffing 方程周期解的研究已经有了许多 结果 [16][17][18] . Nakajima [18] 在超线性条件…”