算子方程

In this paper, we use the coupled fixed point theorem for mixed monotone condensing operators to obtain an existence, uniqueness and iterative approximation theorem of solutions of initial value problems for second order mixed monotone type of impulsive differential equations.

利用混合单调凝聚算子的耦合不动点定理，给出了二阶混合单调型脉冲微分方程的初值问题的解的存在唯一性及迭代逼近定理。

Then by using the Riemann's function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

Then by using the Riemanns function of the operator and constructing an auxiliary problem, an integrodifferential equation equivalent to former problem is got.

然后利用该算子的Riemann函数，通过构造辅助问题，得到了一个等价积分微分方程。

And the general thoughts in which we can deal with the nonlinear integro-differential equations in Banach space.

全文共分为三章，在第一章中，我们对具有凹凸性的非线性算子的研究现状及我们在本文中将要做的工作进行了阐述；同时给出了我们处理本文所讨论的非线性积分-微分方程的总体思路。

The existence of solutions for multi-point boundary value problem with p-Laplacian operator is investigated by using monotone iterative method, h is proved that boundary value problem has at least one positive solution under suitable conditions.

研究带p-Laplace算子的非线性微分方程的多点边值问题解的存在性，应用单调迭代，给出了这类边值问题存在解的充分条件，还给出了向正解靠近的单调集。

In this paper perturbation of eigenvalue and eigenfunction for higher order ordinary differential equation in the case of boundary perturbation combined with operator perturbation we considered.

本文研究了在边界和算子摄动相结合的情况下高阶常微分方程特征值与特征函数的摄动，把摄动问题A_6，μ的特征值λ_ε，μ和特征函数y_6，μ按两参数ε、μ的次幂展开，并且证明这些展开式当ε、μ充分小时是收敛的。

Preserved-amplitude migration ; One-way wave equation ; Fourier finite difference ; Migration operator ; Boundary conditions ; Imaging conditions

保幅偏移；单程波方程；傅里叶有限差分；偏移算子；边界条件；成像条件

Finaly, in the case of the nonlinearities being singular at 0, by utilizing the mountain-pass theorem and some other variational methods, we get the existence of nontrivial solutions of the equations under the Dirichlet boundary condition, where the operator diva(x,u is the p-Laplacian.

最后，我们通过应用山路引理等变分方法，研究当算子diva(x，▽u为p-Laplacian并且非线性项在原点有奇异性时，方程在Dirichlet边值条件下非平凡解的存在性。

In this dissertation,we investigate systematically somefundamental problems concerning the Cauchy problem for linear operatordifferential equations.

在本文中，我们就抽象空间中线性算子微分方程Cauchy问题的一些基本问题进行比较系统的研究，主要的工作是

Based on a 2×2 eigenvalue problem, a 3×3 Lenard pair of operators and a new 1+1 dimensional soliton hierarchy are presented.

本文立足于一个2×2谱问题，获得了3×3 Lenard算子对，并由此导出一类非平凡的(1+1)维孤子方程族。

The split between the two groups can hardly be papered over.

这两个团体间的分歧难以掩饰。

This approach not only encourages a greater number of responses, but minimizes the likelihood of stale groupthink.

这种做法不仅鼓励了更多的反应，而且减少跟风的可能性。