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On periodic solutions for even order differential equations

Nonlinear Analysis: Theory, Methods & Applications, 2008
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Chen, Jinhai, O'Regan, Donal
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Disconjugacy Criteria for Nonselfadjoint Differential Equations of Even Order

Canadian Journal of Mathematics, 1971
Disconjugacy criteria have been established for linear selfadjoint differential equations of order 2n by Sternberg [4] and Ahlbrandt [1]. Such differential equations can be written in the form1.1where it is assumed that the coefficients are real and that Pn(x) ≠ 0.
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Oscillation criteria for even order differential equations

Annali di Matematica Pura ed Applicata, 1964
Three theorems concerning oscillatory properties of solutions of even order ordinary differential equations are given. One theorem gives sufficient conditions for all solutions of (*) y(2n)(x) + f(y(x))p(x) = 0 to possess an infinite number of zeroes on the positive x axis.
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Oscillation Criteria for Even Order Nonlinear Damped Differential Equations

Acta Mathematica Hungarica, 2002
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Oscillation Theorems for Nonlinear Ordinary Differential Equations of Even Order

Canadian Mathematical Bulletin, 1981
Consider the differential equation1wherenis even andf(t, y)is subject to the following conditions:(a)f(t, y)is continuous on [0, ∞)×R;(2) (b)f(t, y)is nondecreasing inyfor each fixedt∈[0,∞);(c)yf(t, y )> 0 fory≠ 0 andt∈[0,∞).
Kreith, Kurt, Kusano, Takasi
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On periodic solutions of even-order ordinary differential equations

Annali di Matematica Pura ed Applicata (1923 -), 2001
The authors investigate the problem of the existence and uniqueness of a periodic solution with a preassigned period \(\omega>0\) for the differential equation \[ u^{(2m)}=f(t,u,u',\ldots,u^{(m-1)}), \tag{1} \] where \(m\geq1\) and the function \(f:\mathbb{R}\times\mathbb{R}^{2m}\to\mathbb{R}\) satisfies the local Catathéodory conditions and is ...
Kiguradze, Ivan, Kusano, Takâsi
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Oscillatory Behavior for Even-Order Nonlinear Functional Differential Equations

Applied Mechanics and Materials, 2013
In this paper, some sufficient conditions are obtained by discussing the oscillatory behavior of solutions for a class of even-order nonlinear functional differential equations, and our results generalize and improve some known results.
Quan Xin Zhang, Li Gao, Chun Xia Li
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Differential algebra of the “even order Korteweg–De Vries equations”

Proceedings of the Edinburgh Mathematical Society, 1990
In the quotient ring of differential polynomials modulo cubic terms the usual odd order hierarchy of Korteweg–de Vries equations can be supplemented by an even order hierarchy. The full (even and odd) sequence is generated by an Olver recursion operator of order one and any pair has zero bracket in the quotient ring.
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