查询词典 nontrivial solution

The well-known invariant subspace problem is A long-standing problem in operator theory,which has been to determine whether every operator $T$ on a Banach space $X$ must have a nontrivial invariant subspace.

不变子空间问题是一个尚未解决的问题， Enflo反例所给出的没有不变子空间的算子不为任何算子的共轭。

A complete novel assumption is presented. Then, we prove the existence of two nontrivial solutions for a class of second order superlinear difference systems with the help of Minimax principle and Linking theorem in critical point theory,.6. Two applications in physics are given. Firstly, a coupled differential system coming from second harmonic waves is discussed.

利用Ricceri建立的三临界点定理，证明了一类含参数二阶差分方程在某些新的条件下至少存在三个解；随后，利用临界点理论中的极小极大原理和环绕定理，讨论了一类二阶超线性差分方程组多重解的存在性。

In this paper, we study the existence of sign-changing and multiple nontrivial solutions for a kind of quasilinear elliptic equations with Dirichlet boundary value by applying minimax methods and Morse theory.

本文我们将应用极大极小方法和Morse理论研究一类拟线性椭圆方程Dirichlet边值问题多解的存在性和解的变号性质。设Ω是R~N(N≥1)中的有界区域，具有光滑边界？

It can be divided into two chapters.In chapter one ,we state a few usual notations,definitions and basic results.In chapter two, we first establish a Morse index theory for 2p-order linear Hamiltonian systems.Then as applications of the index theory ,we discuss nontrivial solutions for nonlinear Hamiltonian systems by making use of Leray-Schauder degree theory and Morse theory.

全文分为两章：第一章中给出了本文所要用到的一些基础知识和一些常用的记号；第二章先建立了线性2p-阶Hamiltonian系统的指标；作为此分类指标的应用，结合Leray-Schauder度理论及Morse 理论，讨论了渐近线性系统的非平凡解的存在性。

By discussing the trivial and nontrivial solutions,and then we discuss the solvability for nonhomogeneous equation.

在第三章中，我们通过对齐次p-Laplacian 方程的平凡解与非平凡解的讨论，建立指标分类理论。

The major technique to get the information of structure of those free groups is to sudy the action of automorphisms on them. In this paper we show that every normal automorphism of a nontrivial free product of groups is inner as well. Traub[16] made a purely algebraic conjecture and showed that it implied Poincare"s Conjecture. He also showed that Poincare"s Conjecture implied this algebraic conjecture modulo another topological hypothesis.

在本文中我们给出任意两个非平凡群的自由积的每个正规自同构也是内自同构的；在文献[16]中，Traub给出了一个纯代数的猜想并证明了这个猜想蕴含着着庞加莱猜想的成立，并且作者也证明了在一个拓扑假设的前提下庞加莱猜想也同时蕴涵着猜想1是成立的，后来这个拓扑假设被Waldhausen([7])证明是成立的。

And we show that if such a immersion is also semi-parallel, it must be totally geodesic. Moreover the same results hold for semi-symmetric submanifolds in a nontrivial complex-space-form.

我们证明了如果它还是半平行的，则它必是全测地浸入，而且这一结果对于复射影空间和复双曲空间中的半对称浸入也成立。

Halin graph is a nontrivial generalization of tree and ring network.

Halln图是对树和环网络的非平凡概括，因此求赋权Halin图的OHP问题是非常有意义的。

The trefoil is known as the simplest nontrivial molecular knot. The C30 carbyne trefoil knot studied is intertwined by the sp hybridized15 chain, which is topologically chiral and belongs to D3 point-group of symmetry.

三叶结分子是最简单的非平凡纽结分子，C30卡宾三叶结分子是由一条闭合的l5 sp杂化碳链组成的，是具有D3对称性的拓扑手性分子。

A survey of duadic codes is presented firstly, necessary and sufficient conditions for the existence of nontrivial duadic abelian codes over Z_4 are presented secondly.

文中首先综述duadic码；其次给出了Z4上存在非平凡duadic阿贝尔码的充分必要条件；最后给出了Z4上劈分为μ-1的非平凡duadic阿贝尔码存在的充分必要条件，这些条件也是存在Z4上非平凡自偶阿贝尔码的充分必要条件。

Putt your way through 36 fun-filled holes of minigolf on 3D designed courses with elevated greens, bunkers, bridges and water hazards, among other crazy obstacles.

您的推杆方式，通过36个有趣的填孔迷你的三维设计的课程，以提升绿党，掩体，桥梁和水的危害，除其他疯狂的障碍。

Some participles can be used either as attributes or as predicatives.

有些分词既可当定语用，也可当表语用。