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

In this paper, the Liénard equation with a deviating argument

x^″(t)+_f1(t,x(t))x^′(t)+_f2(x(t))(x^′(t))²+g(t,x(t−τ(t)))=p(t)$x^{″}\left(t\right)+f_1(t,x\left(t\right))x^{\prime }\left(t\right)+f_2\left(x\left(t\right)\right){\left(x^{\prime }\left(t\right)\right)}^2+g(t,x(t-\tau \left(t\right)))=p\left(t\right)$

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 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,     

New results on the existence of periodic solutions to a p-Laplacian differential equation with a deviating argument

By means of Mawhin's continuation theorem, a kind of p-Laplacian differential equation with a deviating argument as follows:

(φp(x^′(t))^)′=f(t,x(t),x(t−τ(t)),x^′(t))+e(t)     

Periodic solutions for higher order differential equations with deviating argument

By using the coincidence degree theory of Mawhin, we study the existence of periodic solutions for higher order differential equations with deviating argument . Some new results on the existence of periodic solutions of the equations are obtained. Meanwhile, an example is given to illustrate our results.     

Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument

By means of Mawhin's continuation theorem, we study some second order differential equations with a deviating argument:

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

Periodic solutions for p-Laplacian neutral functional differential equation with deviating arguments

By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with deviating arguments such as (φp(x^′(t)−cx^′(t−σ)))+g(t,x(t−τ(t)))=p(t), a result on the existence of periodic solutions is obtained.     

时滞三阶微分方程周期解存在性的充分条件

我们利用Mawhin重合度拓展定理,研究了一类时滞三阶微分方程解的存在性问题,得到了其存在2π周期解的新的结果.值得关注的是,我们允许滞量r是一个函数,并且所得结论与时滞ι(t)有关.同时给出一个实例来论证我们的结果.     

Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments

By using the theory of coincidence degree, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with multiple deviating arguments, a new result on the existence of periodic solutions is obtained.     

Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with finitely many deviating arguments

In this paper, we consider a kind of Rayleigh equation with finitely many deviating arguments of the form

     

Periodic solutions for Liénard type p-Laplacian 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 Liénard type p-Laplacian equation with a deviating argument of the form:

(_?p(x^′(t)))^′+f(x(t))x^′(t)+g(t,x(t-τ(t)))=e(t).$({?}_p(x^{\prime }(t)){)}^{\prime }+f(x(t))x^{\prime }(t)+g(t,x(t-\tau (t)))=e(t)\text{.}$

Periodic solutions for a kind of Liénard equation

Using inequality techniques and coincidence degree theory, new results are provided concerning the existence and uniqueness of T-periodic solutions for a Liénard equations with delay. An illustrative example is provided to demonstrate that the results in this paper hold under weaker conditions than existing results, and are more effective.     

时滞Liénard方程的周期解

利用重合度理论中的延拓定理讨论一类时滞Liénard方程x¨+f(x)x·+g(∫^0_(-r)x(t+s)dm(s))=p(t)的周期解问题. 获得了存在周期解的单侧限制的条件     

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:

Regularity of solutions of evolution integrodifferential equations with deviating argument

In this paper we prove the existence of mild and classical solutions of delay integrodifferential equation and delay integrodifferential evolution equations with nonlocal condition in Banach spaces. The regularity solutions of integrodifferential evolution equations interconnected with viscoelastic material is derived to guarantee the stabilization. The results are established by using the resolvent operators and the fixed point principles. Finally, an example is given to show the potential of the proposed techniques.     

一类具多偏差变元的p-Laplacian方程周期解的存在性

研究了一类具多偏差变元的p-Laplacian方程,为了得到该方程周期解的先验估计,运用分析技巧建立了一些新的不等式,进而利用Mawhin连续定理得到了这类方程周期解的存在性,得到了一些新的结果,推广和改进了已有结果.     

Periodic solutions for a kind of second order neutral functional differential equations

In this paper, criteria are established for the existence of periodic solutions to a second order sublinear neutral differential equation. Our method is based on careful a priori estimation and continuation theorem, and our sublinear condition is an improvement of the boundedness condition in some recent results.     

Periodic solutions for Liénard type p-Laplacian equation with two deviating arguments

In this paper, the Liénard type p$p$-Laplacian equation with two deviating arguments

(_φp(x^′(t)))^′+f(x(t))x^′(t)+_g1(t,x(t−_τ1(t)))+_g2(t,x(t−_τ2(t)))=e(t)${\left({\phi }_p\left(x^{\prime }\left(t\right)\right)\right)}^{\prime }+f\left(x\left(t\right)\right)x^{\prime }\left(t\right)+g_1(t,x(t-{\tau }_1\left(t\right)))+g_2(t,x(t-{\tau }_2\left(t\right)))=e\left(t\right)$

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