3) Method of upper and lower solutions
上下解方法
1.
In this paper,we discuss the existence of solution for fourth-order boundary value problems by using method of upper and lower solutions and maximum principle,where nonlinear term is Caratheodory function up to one side Lipschitz condition.
利用上下解方法和最大值原理讨论了四阶边值问题解的存在性。
2.
In this paper, the method of upper and lower solutions and the fixed point theorem are used to investigate the existence of extremal solution of PBVP for second-order discontinuous differential equation with dependence on first derivative.
利用上下解方法和不动点定理,给出了含导数项的不连续二阶非线性微分方程周期边值问题的极解。
4) the method of upper and lower solutions
上下解方法
1.
In this paper,we make use of the method of upper and lower solutions,cone theory,the Schauder-fixed point theorem,Amann theorem and mapping degree theory to study the Sturm-Liouville boundary value problems,and obtain existence conclutions which have multiple nongenative solutions under some certain conditions.
利用上下解方法,锥理论,Schauder不动点定理,Amann不动点定理以及映射度理论研究Sturm-Liouville边值问题(SL。
2.
By using the method of upper and lower solutions,the periodic boundary value problem for first-order impulsive delay differential equations is considered,and the existence of the maximal and minimal solutions is obtained.
利用上下解方法及单调迭代技巧,讨论了一类一阶脉冲时滞微分方程的周期边值问题,获得了其极大解与极小解的存在性,这样可将方程的解控制在极小解与极大解之间。
5) Upper and Lower solutions
上下解方法
1.
By using Upper and Lower solutions method,Leray-Schauder degree theory and Differential inequality method,we establish the existence and uniqueness theorems for a kind of nth-order nonlinear two-point boundary value problems with weaker Nagumo condition, and we give an example to demmonstrate our results.
本文利用Leray-schauder度理论,上下解方法及微分不等式方法等,在较弱的Nagumo条件下得到了一类n阶非线性两点边值问题解的存在性与唯—性结果,并给出了应用举例。
2.
Based on the upper and lower solutions method,under suitable conditions,existence of solution of a three-point boundary value problem forthird-order ordinary differential equation with nonlinear mixed boundary conditions is obtained.
基于上下解方法,在一定条件下,得到了一类带有非线性混合边界条件的三阶常微分方程的非线性三点边值问题解的存在性,作为上述存在性结果的应用,在推论中给出了一类三阶非线性微分方程三点边值问题解的存在性。
3.
And based on the principle,the existence of the solution to the corresponding nonlinear boundary value problems is proved by taking advantage of the upper and lower solutions method.
讨论了一类偶数阶微分算子的最大值原理,基于该原理用上下解方法证明了相应的非线性边值问题解的存在性,在某些附加条件之下,可以建立一种单调迭代的方法来求解这类问题,给出的例子强调了结果的有效性。
6) upper and lower solution method
上下解方法
1.
Aimed at the mathematic problem in the model of the pendulum oscillation,the paper introduces the study on the existence of odd-harmonic solutions to second order semi-linear differential equation which describes the model of the pendulum oscillation by using upper and lower solution method monotone iterative technique and the Schauder fixed point theorem respectively.
针对摆型振动模型中的数学问题,分别采用上下解方法、单调迭代法及Schauder不动点定理研究了摆型振动模型的二阶半线性微分方程奇调和解的存在性。
2.
Using the Leray-Schauder theory and upper and lower solution method,the existence of solutions for general initial value problem of first order differential equationx′(t)=f(t,x(t)),a.
运用Leray-Schauder原理和上下解方法,讨论了一阶常微分方程广义初值问题x′(t)=f(t,x(t)), a e t∈[0,T],x(0)+∫T0a(t)x(t)dt=c解的存在性。
3.
Applying upper and lower solution method,we investigate the existence of solutions of a class of periodic boundary value problems for impulsive differential equations with piecewise constant argument.
利用上下解方法 ,研究了一类具逐段常数变元的脉冲微分方程的周期边值问题的解的存在
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