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1.
Applying the generalized maximum principle, a Liouvilletype theorem of subharmonic functions on complete Riemannian manifolds is shown and a Liouville-type differential inequality on properly immersed complete submanifolds is given. Project supported by the National Natural Science Foundation of China and K.C. Wong Educational Fund  相似文献   

2.
Using the theory of invariant manifolds, we give local expressions of the stable and unstable manifolds for normally hyperbolic invariant tori, and study the existence of transverse orbits heteroclinic to hyperbolic invariant tori. These extend and improve the corresponding results obtained in [3–5].Supported by the National Natural Science Foundation of China and Shanghai Natural Science Foundation.  相似文献   

3.
A mod 2 index theorem for the twisted Signature operator on 4 q + 1 dimensional manifolds is established. This result generalizes a result of Farber and Turaev, which was proved for the case of orthogonal flat bundles, to arbitrary real vector bundles. It also provides an analytic interpretation of the sign of the Poincare-Reidemeister scalar product defined by Farber and Turaev. Project partially supported by the National Natural Science Foundation of China (Grant No. 19525102), the Fok Ying-Tung Foundation and the Qiu Shi Foundation.  相似文献   

4.
The concept of quasi-adequate transversals is introduced. Some properties and characterizations for abundant semigroups with a multiplicative quasi-adequate transversal are obtained. In particular, a structure theorem for such abundant semigroups is given. Finally, some special cases are considered. This research was partially supported by the National Natural Science Foundation of China (No. 10571077) and the Natural Science Foundation of Gansu Province (No. 3ZS052-A25-017).  相似文献   

5.
We introduce a notion of cobordism of Callias-type operators overcomplete Riemannian manifolds and prove that the index is preserved by such a cobordism. As an application, we prove a gluing formula for Callias-type index. In particular, a usual index of an elliptic operator on a compact manifold can be computed as a sum of indexes of Callias-type operators on two noncompact but topologically simpler manifolds. As another application, we give a new proof of the relative index theorem for Callias-type operators, which also leads to a new proof of the Callias index theorem.  相似文献   

6.
By using Krasnoselskii‘s fixed-point theorem on a suitable cone, several existence results and corresponding properties of positive solutions of nonlocal boundary value problem for nonlinear retarded differential equation are obtained.  相似文献   

7.
A theorem on the transcendency, for a limit of a sequence of algebraic numbers, is given and used to test the transcendencies of some classes of numbers. Project supported by the National Natural Science Foundation of China and the Natural Science Foundation of Zhejiang Province.  相似文献   

8.
This paper introduces the concept of the generalized Riesz operators and the concept of the generalized West decomposition of a general operator which generalizes the definition of the West decomposition of Riesz operators, and proves that the following three statements are equivalent on a general Banach space: (a) Every generalized Riesz operator has the generalized West decomposition; (b) Every operator makes strong Stampfli theorem true; Every operator has Apostol's compact correction.  相似文献   

9.
We discuss the implications of superrigidity and Ratner’s theorem on invariant measures on homogeneous spaces for understanding the fundamental group of manifolds with an action of a semisimple Lie group. Research partially supported by the National Science Foundation and the Israel-U.S. Binational Science Foundation.  相似文献   

10.
We prove the Arnold conjecture for a product of finitely many monotone symplectic manifolds and Calabi-Yau manifolds. The key point of our proof is realized by suitably choosing perturbations of the almost complex structures and Hamiltonian functions for the product case. Supported by the National Natural Science Foundation of China  相似文献   

11.
In this paper, the stability of the set of solutions for symmetric vector quasi-equilibrium problems is discussed. Then, we prove a generic stability theorem and give an existence theorem for essentially connected components of the set of solutions for symmetric vector quasi-equilibrium problems. Finally, we apply these results to vector weak saddle point problems with constraints. This research was partially supported by the Natural Science Foundation of China (Grant number: 10561007) and Natural Science Foundation of Jiangxi Province, China.  相似文献   

12.
Estimations on dimensions of spaces of Jacobi forms are given by extending the classical Siegel theorem to the theory of Jacobi forms. Project supported by the China Postdoctoral Science Foundation and the National Natural Science Foundation of China.  相似文献   

13.
In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm-Liouville boundary value problems for nonlinear second order impulsive differential equations in Banaeh spaces.  相似文献   

14.
Feng Gu 《Positivity》2008,12(3):503-509
The purpose of this paper is to prove a strong convergence theorem for a finite family of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in the paper improve and extend some recent results in Chang [1], Cho et al. [2] Ofoedu [5], Schu [7] and Zeng [8, 9]. The present studies were supported by “the Natural Science Foundation of China (No. 10771141),” the Natural Science Foundation of Zhejiang Province (Y605191), the Natural Science Foundation of Heilongjiang Province (A0211), the Scientific Research Foundation from Zhejiang Province Education Committee (20051897).  相似文献   

15.
This paper establishes a local limit theorem for solutions of backward stochastic differential equations with Mao's non-Lipschitz generator, which is similar to the limit theorem obtained by [3] under the Lipschitz assumption.  相似文献   

16.
In the paper, by using Ky Fan’s section theorem, we obtain an existence theorem for vector equilibrium problems. Motivated by the ideas of Kinoshita and McLennan, we introduce the concept of the essential component of the solution set for vector equilibrium problems, and we prove that there exists at least one essential component of the solution set for every vector equilibrium problem satisfying some conditions. Research was partially supported by the Natural Science Foundation of Guangdong Province, P. R. China.  相似文献   

17.
We establish a comparison-estimate of the second Rauch type for Ricci curvature. As an application, we get a result of local splitting for Riemannian manifolds. This work is partly supported by the National Natural Science Foundation (10371047) of China.  相似文献   

18.
Symmetric strong vector quasi-equilibrium problems   总被引:2,自引:0,他引:2  
In this paper, we introduce the symmetric strong vector quasi-equilibrium problem. We then demonstrate that the symmetric strong vector quasi-equilibrium problem is solvable under the suitable assumptions. As an application, we get an existence theorem of the strong saddle points of vector-valued functions. In addition, we give a characterization of vector-valued properly quasi-convex functions. This work was supported by the Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China  相似文献   

19.
By constructing a special cone and using cone compression and expansion fixed point theorem, this paper presents some existence results of positive solutions of singular boundary value problem on unbounded domains for a class of first order differential equation. As applications of the main results, two examples are given at the end of this paper. Supported by the National Natural Science Foundation of China (No. 10671167) and the Natural Science Foundation of Liaocheng University (31805).  相似文献   

20.
In this paper, Stampacchia generalized vector quasiequilibrium problem and generalized vector loose saddle points for set-valued mappings are introduced. By using the scalarization method and the fixed-point theorem, existence theorems are established.This work was supported by the National Natural Science Foundation of China and the Natural Science Foundation of Jiangxi Province, China. The author is grateful to Professor F. Giannessi and the referee for valuable comments and careful reading improving the original draft.Communicated by F. Giannessi  相似文献   

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