Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps...Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps on B(X)preserving Fredholm operators with fixed nullity or defect equal to n in both directions,and describe completely the structure of these maps.展开更多
In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linea...In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.展开更多
The purpose of this article is to present Schechter’s manner to introduce α-Wayl operators and compare this definition with another one given by Yadav and Arora. Moreover, we introduce generalized Weyl operator in t...The purpose of this article is to present Schechter’s manner to introduce α-Wayl operators and compare this definition with another one given by Yadav and Arora. Moreover, we introduce generalized Weyl operator in the way that we keep many properties of the class of Weyl operators.展开更多
The paper presents a holomorphic operator function approach for the transmission eigenvalue problem of elastic waves using the discontinuous Galerkin method.To use the abstract approximation theory for holomorphic ope...The paper presents a holomorphic operator function approach for the transmission eigenvalue problem of elastic waves using the discontinuous Galerkin method.To use the abstract approximation theory for holomorphic operator functions,we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero.The convergence for the discontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator.The spectral indicator method is employed to compute the transmission eigenvalues.Extensive numerical examples are presented to validate the theory.展开更多
This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,s...This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.展开更多
In this paper,we define mean index for non-periodic orbits in Hamiltonian systems and study its properties.In general,the mean index is an interval in R which is uniformly continuous on the systems.We show that the in...In this paper,we define mean index for non-periodic orbits in Hamiltonian systems and study its properties.In general,the mean index is an interval in R which is uniformly continuous on the systems.We show that the index interval is a point for a quasi-periodic orbit.The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schr¨odinger operators.Motivated by their works,we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper.展开更多
In this paper,we study an m-point boundary value problem of third order ODEs at resonance. We prove some existence results for the m-point boundary value problem at resonance by the coincidence degree theory of [8,9]....In this paper,we study an m-point boundary value problem of third order ODEs at resonance. We prove some existence results for the m-point boundary value problem at resonance by the coincidence degree theory of [8,9]. Our result is new. Meanwhile,an example is presented to demonstrate the main result.展开更多
基金supported by National Natural Science Foundation of China(11771261,11701351)Natural Science Basic Research Plan in Shaanxi Province of China(2018JQ1082)the Fundamental Research Funds for the Central Universities(GK202103007,GK202107014).
文摘Let X be an infinite-dimensional real or complex Banach space,and B(X)the Banach algebra of all bounded linear operators on X.In this paper,given any non-negative integer n,we characterize the surjective additive maps on B(X)preserving Fredholm operators with fixed nullity or defect equal to n in both directions,and describe completely the structure of these maps.
文摘In this paper we use the notion of measure of non-strict-singularity to give some results on Fredholm operators and we establish a fine description of the Schechter essential spectrum of a closed densely defined linear operator.
文摘The purpose of this article is to present Schechter’s manner to introduce α-Wayl operators and compare this definition with another one given by Yadav and Arora. Moreover, we introduce generalized Weyl operator in the way that we keep many properties of the class of Weyl operators.
基金supported in part by the National Natural Science Foundation of China with Grant No.11901295Natural Science Foundation of Jiangsu Province under BK20190431+1 种基金partially supported by the National Natural Science Foundation of China with Grant No.11971468Beijing Natural Science Foundation Z200003,Z210001.
文摘The paper presents a holomorphic operator function approach for the transmission eigenvalue problem of elastic waves using the discontinuous Galerkin method.To use the abstract approximation theory for holomorphic operator functions,we rewrite the elastic transmission eigenvalue problem as the eigenvalue problem of a holomorphic Fredholm operator function of index zero.The convergence for the discontinuous Galerkin method is proved following the abstract theory of the holomorphic Fredholm operator.The spectral indicator method is employed to compute the transmission eigenvalues.Extensive numerical examples are presented to validate the theory.
基金supported by National Natural Science Foundation of China (grant No.41874132)supported by National Natural Science Foundation of China (grant No.11201173)+3 种基金National Natural Science Foundation of China (grant No.11171132,grant No.11571065)Science and Technology Developing Plan of Jilin Province (grant No.20180101220JC)supported by National Basic Research Program of China (grant No.2013CB834100)Jilin DRC (grant No.2017C028-1)。
文摘This paper concerns the controllability of autonomous and nonautonomous nonlinear discrete systems,in which linear parts might admit certain degeneracy.By introducing Fredholm operators and coincidence degree theory,sufficient conditions for nonlinear discrete systems to be controllable are presented.In addition,applications are given to illustrate main results.
基金supported by National Key R&D Program of China(Grant No.2020YFA0713300)NSFC(Grant Nos.12071255,11790271)the second author is partially supported by NSFC(Grant Nos.12071255,11425105)。
文摘In this paper,we define mean index for non-periodic orbits in Hamiltonian systems and study its properties.In general,the mean index is an interval in R which is uniformly continuous on the systems.We show that the index interval is a point for a quasi-periodic orbit.The mean index can be considered as a generalization of rotation number defined by Johnson and Moser in the study of almost periodic Schr¨odinger operators.Motivated by their works,we study the relation of Fredholm property of the linear operator and the mean index at the end of the paper.
基金sponsored by the National Natural Science Foundation of China (10671023)the Scientific Creative Platform Foundation of Beijing Municipal Commission of Education (PXM2008-014224-067420)the Science Foundation of Ministry of Education of Beijing (KM200810772010)
文摘In this paper,we study an m-point boundary value problem of third order ODEs at resonance. We prove some existence results for the m-point boundary value problem at resonance by the coincidence degree theory of [8,9]. Our result is new. Meanwhile,an example is presented to demonstrate the main result.
