1) Confliction Theory
域重合理论
2) Theory of coincidence degree
重合度理论
1.
The theory of coincidence degree is used to study the second order differential equation x″(t)+ax′(t)+bx(t)+g(x(x(t)))=p(t), which has complex deviating arguments,and the main theory about periodic solutions to this equation is provided.
用重合度理论研究了二阶的具有复杂偏差变元的Duffing型方程x″(t)=ax′(t)+bx(t)+g(x(x(t)))=p(t),得到其周期解的存在性。
2.
In this paper,the theory of coincidence degree is used to study the existence of a periodic solution for the differential equation with delayax″(t)+cx′(t)+bx(t)+g(x(t-τ(t)))=p(t)and a sufficient theorem is obtained for the existence of a periodic solution of of the equation.
用重合度理论研究一类时滞微分方程ax″(t)+cx′(t)+bx(t)+g(x(t-(τt)))=p(t)周期解的存在性,得到了该方程存在T(T>0)周期解存在的充分性定理。
3.
By using the theory of coincidence degree,we study periodic solutions for a kind of second order neutral functional differential equations(x(t)-cx(t-σ))″+g(t,x(t-τ(t)))=p(t).
利用重合度理论,研究一类二阶中立型泛函微分方程(x(t)-cx(t-σ))″+g(t,x(t-τ(t)))=p(t)的周期解的存在性,得到了周期解存在的新的结果。
3) continuation theorem
重合度理论
1.
By means of continuation theorem of coincidence degree theory,the authors study a class of second order differential equation with multiple deviating arguments x″(t)+f(t,x(t),x(t-τ0(t)),x′(t))+∑ from j=1 to n g(x(t-τj(t)))=p(t) Some new results on the existence f periodic solution are obtained.
本文利用重合度理论研究了一类二阶多偏差变元的微分方程x″(t)+f(t,x(t),x(t-τ0(t)),x′(t))+∑ from j=1 to n g(x(t-τj(t)))=p(t)的周期解问题,得到了存在周期解的新的结果。
2.
By means of Mawhin s continuation theorem, we studied a kind of third order functional differential equation with deviating arguments in the following form: and some new results on the existence of 2π-periodic solutions are obtained.
利用重合度理论研究一类三阶具偏差变元微分方程c(t)x′′′(t)+(∑|i=0|2)[aix(i)2k-1(t)+bix(i)2k-1(t-τi)]+g1(x(t))+g2(x(t-τ(t)))=p(t)的2π-周期解问题,得到了其存在2π-周期解的一些新的结果。
3.
By employing the continuation theorem of coincidence degree theory,we study a kind of third order functional differential equation with a deviating argument as follow:x(t)+ax″(t)+bx′(t)+cx(t)+g(x(t-τ(t)))=p(t).
利用重合度理论研究一类三阶具偏差变元微分方程x(t)+ax″(t)+bx′(t)+cx(t)+g(x(t-τ(t)))=p(t)的2π-周期解问题,得到了存在2π-周期解的充分条件。
4) coincidence degree
重合度理论
1.
Existence of periodic solutions for higher order functional differential equation is consider,by using the theorem of coincidence degree,the sufficient conditions for its there being at least a T-periodic solution is obtained.
利用重合度理论,研究了一类具偏差变元高阶L ienard型方程周期解的存在性,获得了该方程至少存在一个周期解的充分条件。
2.
In the second part, we will prove the persistence of the system and find the conditions for the existence of periodic solutions by using the Gaines and Mawhin\'s continuation theorem of coincidence degree theory.
本文将研究一类含有时滞的基于比率依赖的非自治捕食者-食饵扩散系统,在第二章证明该系统的一致持久性,并利用Gaines和Mawhin的关于重合度理论的连续性定理,建立模型正周期解的存在性条件。
3.
By using the theorem of coincidence degree,a class of second order neutral functional differential equation with infinite delay is studied.
利用重合度理论研究了一类具有无穷时滞二阶中立型泛函微分方程,获得了周期解存在的一些新的结果。
5) coincidence degree theory
重合度理论
1.
Using coincidence degree theory,sufficient conditions are obtained that ensure the existence of multiple positive periodic solutions for a discrete general predator-prey system.
运用重合度理论的方法,得到一个具有时滞的捕食者-食饵一般离散系统多个周期解存在所需满足的必要条件,从而有利于更好地研究生物种群的持续生存。
2.
By means of better prior estimate and the coincidence degree theory,we study the existence of periodic solutions for a kind of high-order differential equation with delay shch as (x(t)-cx(t-σ))(n)+∑n-1i=2aix(i)(t-δi)+g(t,x(t-r(t))=f(t,x(t-τ(t)),x′(t-δ(t)))+p(t) Some new sufficient condition of periodic solutions is obtained on the even more conditions.
利用更精确的估计和重合度理论,研究了一类具有时滞的高阶微分方程(x(t)-cx(t-σ))(n)+∑n-1i=2aix(i)(t-δi)+g(t,x(t-r(t))=f(t,x(t-τ(t)),x′(t-δ(t)))+p(t)的周期解存在性问题,在更弱的条件下获得了该方程周期解性的若干新的充分条件,推广和改进了已有文献的相关结果。
3.
By using the coincidence degree theory of Mawhin,the existence of solutions for higher order multi-point boundary value problem at resonance is given,where the nonlinear term contain all derivatives.
利用Mawhin的重合度理论,研究具有共振的高阶多点边值问题解的存在性,其中的非线性项含有各阶导数。
6) double control theory and reasonable zone
双控论和合理域
补充资料：超导电性的局域和非局域理论（localizedandnon-localizedtheoriesofsuperconductivity）
超导电性的局域和非局域理论（localizedandnon-localizedtheoriesofsuperconductivity）
伦敦第二个方程（见“伦敦规范”）表明，在伦敦理论中实际上假定了js(r)是正比于同一位置r的矢势A(r)，而与其他位置的A无牵连；换言之，局域的A(r)可确定该局域的js(r)，反之亦然，即理论具有局域性，所以伦敦理论是一种超导电性的局域理论。若r周围r'位置的A(r')与j(r)有牵连而影响j(r)的改变，则A(r)就为非局域性质的。由于`\nabla\timesbb{A}=\mu_0bb{H}`，所以也可以说磁场强度H是非局域性的。为此，超导电性需由非局域性理论来描绘，称超导电性的非局域理论。皮帕德非局域理论就是典型的超导电性非局域唯象理论。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条