泛函性

基本解释 (translations)

functionality

与泛函性相关的网络例句 [注：此内容来源于网络，仅供参考]

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用"超平面"的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的"平移"方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

The contents are the following:In chapter two, the existence and multiplicity results for the following equation of p-Laplacian type are obtained.For the elliptic quasilinear hemivariational inequality involving the p-Laplacian operator,in order to use the mountain pass theorem proving the existence result, the authors usually need to use the uniform convexity of the Sobolev space to prove the energy function satisfies the PS condition. But for the p-Laplacian type equation mentioned above, this method is no use. To overcome this difficulty, the potential function is assumed to be convex, then I prove the existence result and by using the extension of the Ricceri theorem, the multiplicity result for the problem is obtained.

在第二章我们首先考虑关于以下p-Laplacian型(p-Laplacian type)方程非平凡解及多解的存在性对于带有p-Laplacian算子的椭圆拟线性半边分不等式问题，为应用非光滑的山路引理证明解的存在性，在证明方程所对应的能量泛函满足非光滑的PS条件时，需利用Sobolev空间的一致凸性，但是对于具有更一般形式的算子的p-Laplacian型方程，不具备上述性质，在文中为克服这一困难，本人对位势泛函做了一致凸的假设，从而证明了解的存在性，并应用推广的Ricceri定理，证明了方程三个解的存在性。

Firstly, the existence and uniqueness of the solution for neutral stochastic functional differential equations with infinite delay under the uniformly Lipschitz condition, linear grown condition and contractive condition can be directly derived; And the moment estimate of the solution and the estimate for error between the approximate solution and the accurate solution can be both given; If the uniformly Lipschitz condition is replaced by the local Lipschitz condition, the existence and uniqueness theorem can be gained; Meanwhile, the existence and uniqueness of the global solution in the interval 0,+∞ can also be obtained; Secondly, L~p-exponential estimate of the solution for neutral stochastic functional differential equations with infinite delay can be studied; At length, the theorem of the local solution about neutral stochastic functional differential equations with infinite delay only under the local Lipschitz condition and the contractive condition can be established.

首先，在一致Lipschitz条件，线性增长条件和压缩性条件下，直接得到了具无限时滞中立型随机泛函微分方程解的存在惟一性，并给出了解的矩估计，近似解与精确解之间的误差估计；将一致Lipschitz条件替换为局部Lipschitz条件，也得到了具无限时滞中立型随机泛函微分方程解的存在惟—性，同时，也给出了在整个区间0，+∞上具无限时滞中立型随机泛函微分方程解的存在惟一性定理；其次，也讨论了具无限时滞中立型随机泛函微分方程解的L~p指数估计；最后，在局部Lipschitz条件和压缩性条件下，建立了具无限时滞中立型随机泛函微分方程局部解的存在惟一性定理。

First,we consider the lower semicontinuity property fora functional with linear growth in LDΩthe second, in the SBD space,we discussthe lower semicontinuity of an integral functional that the integrand is a Carathéodoryfunction and that satisfies a symmetric quasi-convex assumption, by the compactnesstheorem of the SBD space,blow-up method and Morrey theorem,prove that integral functional is lower semicontinuous with respect to L~1- convergence;then by using theone-dimentional sections method and the structure theorem of the BD functions, dis-cuss the lower semicontinuity of the integral functional in the whole BD space.

首先我们考虑LD空间满足线性增长的积分泛函的下半连续性；其次在SBD函数空间讨论了被积函数为Carathéodory函数时的积分泛函在满足对称拟凸条件时的下半连续性，主要利用SBD函数空间的紧性定理和blow-up方法以及Morrey定理等给出了积分泛函关于L~1-强收敛的下半连续性；然后利用BD函数的一维截断方法和结构定理，讨论了在BD全空间上的积分泛函的下半连续性。

Later, we estimate our variational functional to get a nontrivial solution of the new equation and so the second solution for is obtained.

然后我们利用函数平移将原来的非齐次边界问题转化为奇次边界问题，验证了其对应的变分泛函满足不带条件的山路引理的两个条件，并给出了泛函临界点存在的一个充分条件，最后对具体的变分泛函进行估计，得到了新方程非平凡解的存在性结果，从而得到了原方程第二个正解的存在性结果。

Since the solutions of this problem are the critical points of the associated energy function. One generally needs some compactness such as PScondition or C-condition to prove the existence of critical points of the energy func-tion, but when we study the elliptic equation in R~N, the compactness condition does not always hold since the imbedding of the Sobolev space H_0~(1,2)into L~(2*) is not compact. In this chapter, based on the nonsmooth critical point theory, and by using the approximation technique with periodic function, the existence of nontrivial solution is obtained.

由于该方程的解就是其所对应的能量泛函的临界点，通常都要在一些紧型条件的基础上来证明其所对应的能量泛函临界点的存在性，但当我们在无界域上考虑该椭圆方程解的存在性时，Sobolev空间H_0~(1，2)到L~(2*)的嵌入非紧，从而导致所对应的能量泛函失去紧性，本章在非光滑临界点理论的基础上，应用周期逼近的方法证明该问题非平凡解的存在性。

The positive periodic solution of functional differential equation with infinite delay is deeply concentrated these years, some scholars study this subject by means of Lyapunov theorem, Schauder fixed point theorem, and cone extending and compression theorem (from thesis -[5]), and they obtain the existence theorem of positive periodic solution.

近年来，无穷时滞泛函微分方程的周期解问题受到广泛关注，一些学者应用Lyapunov泛函方法，Schauder不动点方法，以及非线性泛函分析中的锥拉伸锥压缩方法(见[1]-[5])，研究了无穷时滞泛函微分方程的周期解的存在性问题。

We established abstract functional spaces, proved that the plastic deformation power rate functional is strict convex and the friction power rate functional and the tensional stress power rate functional are convex. So, strict convexity of the total power rate functional 〓 can be obtained. Further, By nonlinear analysis theory, we proved the existence and uniqueness of minimal point of functional 〓.

本文首先建立了抽象的泛函空间，证明了塑性变形功率泛函是严格凸泛函，摩擦功率泛函和外力功率泛函是凸泛函，从而得到总能耗率泛函的严格凸性，进一步地，利用非线性分析的理论，得到总能耗率泛函有唯一的极小值点。

In this paper, by using the notable Mountain Pass Lemma of critical point theory, some sufficient conditions for the existence and multiplicity of periodic and subharmonic solutions to a class of second order nonlinear functional difference equations with Jacobi operators are obtained.

论文研究了一类具有Jacobi算子类型的二阶非线性泛函差分方程(1)的周期解和次调和解的存在性与多重性。首先将方程（1）的解的存在性问题转化为某个泛函临界点的存在性问题，然后验证此泛函满足著名的山路引理的条件，从而得到论文的主要结论。

In this paper,making use of hyperplane method,we improve the proof of the separation theorem;On the other hand,we use a new method of moving neighborhood to simplify the proof for the continuity of a subconvex function defined on a convex in a normed linear space.

在巴拿赫空间理论中，Hahn-Banach泛函延拓定理作为泛函分析三大基本定理之一，分隔性定理是Hahn-Banach定理的重要应用，本文利用&超平面&的方法，改进了一个分隔性定理的证明；另外，本文利用邻域的&平移&方法，给出了定义在赋范线性空间内的凸集上的次凸泛函连续性的简捷证明。

与泛函性相关的网络解释 [注：此内容来源于网络，仅供参考]

additive functional transformation：加性泛函变换

additive functional 加性泛函数 | additive functional transformation 加性泛函变换 | additive group 加法群

additive functional：加性泛函数

additive class 加性类 | additive functional 加性泛函数 | additive functional transformation 加性泛函变换

almost additive functional：殆加性泛函

almonry | 施赈所(救济品发放所) | almost additive functional | 殆加性泛函 | almost bounded function | 殆有界函数

local commutativity：局部交换性

局部异常 local anomaly | 局部交换性 local commutativity | 局部密度泛函法 local density functional method

subadditive interval function：次加性区间函数

subadditive functional 次加性泛函 | subadditive interval function 次加性区间函数 | subadditive set function 次加性集函数

superadditive set function：超加性集函数

superadditive functional 超加性泛函 | superadditive set function 超加性集函数 | superadditivity 超加性

subadditive function：次加性函数

sturm liouville eigenvalue problem 斯图谟 刘维尔特盏问题 | subadditive function 次加性函数 | subadditive functional 次加性泛函

subadditive functional：次加性泛函

subadditive function 次加性函数 | subadditive functional 次加性泛函 | subadditive interval function 次加性区间函数

superadditive functional：超加性泛函

superabundance 过剩数 | superadditive functional 超加性泛函 | superadditive set function 超加性集函数

functional Taylor series：泛函泰勒级数

函数切换电路 functional switching circuit | 泛函泰勒级数 functional Taylor series | 函数性 functionality