In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward ...In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.展开更多
In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem...In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem in a suitable Hilbert space,and obtain some pivotal properties of self-adjoint operator.Subsequently,by establishing the boundary condition space and constructing the embedded mapping,we show that the simple eigenvalue branch of this system is not only continuous,but also smooth.We then obtain the differential expressions of the eigenvalue branch in the sense of Frechet derivative.展开更多
基金Supported by National Natural Science Foundation of China(11001130,12272062)Fundamental Research Funds for the Central Universities(30917011335).
文摘In this paper,we investigate the weighted Dirichlet eigenvalue problem of polynomial operator of the drifting Laplacian on the cigar soliton■as follows■where is a positive continuous function on,denotes the outward unit normal to the boundary,and are two nonnegative constants.We establish some universal inequalities for eigenvalues of this problem.
基金Supported by the National Natural Science Foundation of China(12461039)Excellent Graduate Innovation Star Scientific Research Project of Gansu Province of China(2025CXZX-273)。
文摘In this study,we mainly discuss some spectral properties of the Dirac operator with eigenparameter-dependent boundary condition.Initially,we reformulate the spectral problem into linear operator eigenparameter problem in a suitable Hilbert space,and obtain some pivotal properties of self-adjoint operator.Subsequently,by establishing the boundary condition space and constructing the embedded mapping,we show that the simple eigenvalue branch of this system is not only continuous,but also smooth.We then obtain the differential expressions of the eigenvalue branch in the sense of Frechet derivative.
