Existence of periodic solutions for a Liénard type p-Laplacian differential equation with a deviating argument

By means of Mawhin’s continuation theorem, a class of p-Laplacian type differential equation with a deviating argument of the form

(_φp(x^′(t)))^′+f(x(t))x^′(t)+β(t)g(t,x(t−τ(t,_|x|∞)))=e(t)${\left({\phi }_p\left(x^{\prime }\left(t\right)\right)\right)}^{\prime }+f\left(x\left(t\right)\right)x^{\prime }\left(t\right)+\beta \left(t\right)g(t,x(t-\tau (t,{\left|x\right|}_{\infty })))=e\left(t\right)$

On solutions of a neutral differential equation with deviating argument

We prove a theorem on the existence and asymptotic behaviour of solutions of a differential equation with a deviating argument of neutral type. The considered equation contains both delayed and advanced arguments. The method used in the proof of our main result depends on conjunction of the classical Schauder fixed point theorem with the technique of measures of noncompactness.     

Periodic solutions of a nonlinear second-order differential equation with deviating argument

With the help of the coincidence degree continuation theorem, the existence of periodic solutions of a nonlinear second-order differential equation with deviating argument

x^″(t)+f₁(x(t))x^′(t)+f₂(x(t))(x^′(t)⁾²+g(x(t−τ(t)))=0,     

Reducibility of a differential equation with deviating argument to an equation with commensurable constant deviations

Translated from Matematicheskie Zametki, Vol. 44, No. 5, pp. 561–566, November, 1988.     

一类时滞Duffing微分方程同宿解的存在性

利用重合度理论和一些分析技巧,得到一类二阶时滞Duffing微分方程的2kT周期解,通过对该微分方程的一系列周期解取极限获得同宿解的存在性.同时,β(t)是可变号的.     

Existence of periodic solutions for a class of second order differential equation with deviating argument

By means of Mawhin’s continuation theorem, a second order differential equation with a deviating argument is studied. A new result on the existence of periodic solutions is obtained. Meanwhile, the approaches used to estimate a priori bounds of periodic solutions are different from the corresponding ones in the known literature.     

Periodic solutions for a higher order p-Laplacian neutral functional differential equation with a deviating argument

In this paper, a higher order p-Laplacian neutral functional differential equation with a deviating argument:

[φ_p([x(t)−c(t)x(t−σ)]⁽ⁿ⁾)]^(m)+f(x(t))x^′(t)+g(t,x(t−τ(t)))=e(t)     

On a periodic problem for higher-order differential equations with a deviating argument

For higher-order nonautonomous linear and nonlinear differential equations with deviating arguments, new sufficient conditions of existence and uniqueness of a periodic solution are found.     

Periodic solutions for a kind of Rayleigh equation with a deviating argument

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Rayleigh equation with a deviating argument of the form

x^″+f(x^′(t))+g(t,x(t−τ(t)))=p(t).     

Periodic solutions of a functional equation with linearly deviating argument

Translated from Issledovaniya po Prikladnoi Matematike, No. 16, pp. 125–131, 1989.     

New results of periodic solutions for a Rayleigh equation with a deviating argument

In this work, we study the following Rayleigh equation with a deviating argument:

Existence of periodic solutions for a fourth-order -Laplacian equation with a deviating argument

In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:

[φ_p(u^″(t))]^″+f(u^″(t))+g(u(t−τ(t)))=e(t).