把上下解方法应用到相应有限差分系统上，得到两个迭代序列。
Using the method of upper lower solutions we construct two monotone sequences for the finite difference equations.
使用的主要方法有锥上的不动点理论、拓扑度理论和上下解方法等。
Some efficient tools such as topological degree theory, fixed point theory and lower and upper method have been applied.
方法应用单调迭代技术结合上下解方法讨论最大解与最小解的存在性。
Methods The method of upper and lower solutions and the monotone iterative technique were used to establish our results.
方法运用极值原理、上下解方法、分歧理论、线性算子的扰动理论和分歧解的稳定性理论进行研究。
Methods the maximum principle, monotone method, bifurcation theory, the perturbation theorem for linear operators and the stability theorem for bifurcation solutions were used.
利用打靶法、上下解方法和不动点定理等工具，研究有孔区域上一类具非局部边值条件的非线性扩散方程。
The shooting method, sub and super solution method, and fixed point theorem were used to study a class of nonlinear diffusion equations with nonlocal boundary value condition in perforated domains.
本文利用摄动方法和上下解方法，讨论了一类奇异非线性椭圆边值问题，它具有很好的应用背景和理论意义。
In this paper, a singular nonlinear elliptic boundary value problem which is very important in applied science and pure theory was discussed by the method of perturbation, sub-and super-solution.
运用上下解方法，不动点指数理论，局部分歧理论，得出了该系统存在多个正解或惟一正解的条件，即参数对解的个数有一定影响。
By means of lower-upper solutions methods, theory of fixed point indices and local bifurcation theory, the conditions for multiplicity and uniqueness positive solutions of this system was obtained.
利用变形边界函数法与上下解方法，研究了一类具非线性边界条件的半线性时滞微分方程边值问题，得到了此边值问题解的存在性的充分条件。
The asymptotic behavior for a class of higher-order delay partial differential equations be investigated in this paper, some asymptotic behavior be established, which expanded some references.
第二章用上下解的方法来研究耦合半线性抛物方程组的动力学行为，给出了解的渐近行为。
The dynamics of coupled systems of semilinear parabolic equations are investigated using the method of upper and lower solutions. The asymptotic behavior of the solutio is given.
运用正则化方法和上下解技巧证明了上述问题的古典正解的局部存在性及其可延拓性。
The method of regularization and the technique of upper and lower solutions are employed to show the local existence and the continuation of the positive classical solution of the above problem.
方法采用上下解的方法、单调迭代法、比较原理、极值原理以及特征值理论进行了研究。
Methods the upper-lower solutions, monotone derivative methods, the maximum principle, comparison principle and principal eigenvalue theory were used.
我们将利用正则化方法和上下解技巧给出局部古典解和整体古典解的存在唯一性。
We will use regularization method and upper and lower solution technique to give the local existence, global existence and uniqueness results.
对于初值问题，采用上下解的单调迭代方法求解。
Upper lower solutions method and monotone iterative technique are applied to initial value problem.
研究一类四阶微分方程解的存在性，利用上下解及单调迭代的方法，得出这类四阶方程的最大解和最小解的存在。
We obtain the existence of extremal solutions of the boundary value problem by using the method of lower and upper solutions coupled with monotone iterative technique.
构造了一对合适的上下解，利用单调迭代方法证明了模型的两个平衡点之间行波解的存在性，进一步丰富了单调方法的内容。
This paper uses the monotone iterative technique to investigate the existence of the solutions of a class of boundary value problem for third-order differential equation.
构造了一对合适的上下解，利用单调迭代方法证明了模型的两个平衡点之间行波解的存在性，进一步丰富了单调方法的内容。
This paper uses the monotone iterative technique to investigate the existence of the solutions of a class of boundary value problem for third-order differential equation.
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