1) second order differential equation
二阶微分方程
1.
The existence of positive homoclinic orbits is obtained by the variational approach for a class of the second order differential equations-α(x)u+β(x)u2+γ(x)u3=0,where the coefficient functions α(x),β(x),γ(x) satisfy xα′(x)≥0,xβ′(x)≤0,xγ′(x)≤0 for all x∈R.
运用变分方法证明了一类二阶微分方程-α(x)u+β(x)u2+γ(x)u3=0,x∈R的正同宿轨存在性,其中系数函数α(x),β(x),γ(x)满足xα′(x)≥0,xβ′(x)≤0,xγ′(x)≤0对任意x∈R成立。
2.
Research on the solution s existence-uniqueness and singular perturbation for a class of boundary value problem of second order differential equation,using the results obtained,research the singular perturbation for boundary value problem of second order semi-linear differential equation.
研究一类二阶微分方程边值问题的微分不等式理论与解的存在唯一性,利用所得结论研究其二阶拟线性微分方程边值问题的奇异摄动现象。
3.
In this paper,we research the singular perturbation for boundary value problem of second order differential equation with two small parameter as following:{εy″= f(t,y,y′,ε,μ),a < t < by(a,ε,μ) = A(ε,μ),y(b,ε,μ)=B(ε,μ) under the condition of strong stability.
研究在强稳定条件下的具有两个小参数的二阶微分方程的边值问题{εy″=f(t,y,y′,ε,μ),a
2) second-order differential equation
二阶微分方程
1.
Considered were the differential inequality and the existence of solution of the boundary value problem for second-order differential equations that doesn t accord with the Nagumo condition.
在一定的条件下研究一类不具备Nagumo条件的二阶微分方程的边值问题的微分不等式理论及解的存在性。
2.
The periodic boundary value problem for nonlinear second-order differential equations was investigated.
研究一类非线性二阶微分方程的周期边值问题,利用上下解方法,结合单调迭代技巧,得到方程存在解或极值解的充分条件。
3) differential equation of second order
二阶微分方程
1.
The energy eigenvalues of three-dimensional harmonic oscillator and hydrogen atom are solved by using supersymmetric WKB approximate method;the eigenvalue of angular momentum and angular dimension of non-central potential are gained by applying SWKB theory to differential equation of second order including angular coordinate.
运用超对称准经典近似方法给出三维谐振子、氢原子的能谱,进而将该方法用于含角坐标的二阶微分方程,得到角动量平方L2的本征值和非中心势的角向本征值。
2.
In this paper, we studied oscillatory properties of a differential equation of second order and used the differential inequality for coefficient of differential equation to judge oscillation of equation.
研究了一类二阶微分方程的振动性质,利用方程的系数满足的微分不等式来判断方程的振动性。
3.
With the results we studied oscillatory properties of differential equation of second order by using the results.
讨论了一般的 Euler方程解的振动性 ,并利用它研究了二阶微分方程的振动性
4) second order differential equations
二阶微分方程
1.
The problem on stability of second order differential equations with both impulse and delay is investigated.
研究了带脉冲和时滞的二阶微分方程的稳定性问题。
2.
Some oscillation criteria are given for certain second order differential equations by using an integral averaging technique.
利用积分平均技巧研究二阶微分方程(r(t)(x(t) )x′(t) )′+ q(t) f(x(t) ) g(x′(t) ) =0 。
3.
We study some twist second order differential equations.
本文研究了具有扭转性的二阶微分方程,证明在一定条件下通过角函数的扭转所表述的几何性质可以得到周期解的存在性。
6) second-order ordinary differential equation
二阶常微分方程
1.
Second-order ordinary differential equations arise in a wide variety of scientific and engi-neering applications, including celestial mechanics, theoretical physics and chemistry, electronicsand semi-discretisation of partial differential equation.
二阶常微分方程在天体力学、理论物理与化学、电子学以及偏微分方程的半离散等领域具有广泛的应用。
2.
This paper deals with numerical methods for the second-order ordinary differential equations y″(x)=f(x,y) and their numerical stability property.
主要研究二阶常微分方程初值问题y″(x)=f(x,y)的数值方法及其数值稳定性。
补充资料：二阶线性齐次微分方程
二阶线性微分方程的一般形式为
ay"+by'+cy=f(1)
其中系数abc及f是自变量x的函数或是常数。函数f称为函数的自由项。若f≡0，则方程（1）变为
ay"+by'+cy=0（2）
称为二阶线性齐次微分方程，而方程（1）称为二阶线性非齐次微分方程。
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