In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spect...In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.展开更多
We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the...We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.展开更多
基金supported by Natural Science Foun- dation of Jiangsu Province of China (BK 2010489)the Outstanding Plan-Zijin Star Foundation of Nanjing University of Science and Technology (AB 41366)+1 种基金NUST Research Funding (AE88787)the National Natural Science Foundation of China (11071119)
文摘In this paper, the classical Ambarzumyan’s theorem for the regular SturmLiouville problem is extended to the case in which the boundary conditions are eigenparameter dependent. Specifically, we show that if the spectrum of the operator D 2 ＋q with eigenparameter dependent boundary conditions is the same as the spectrum belonging to the zero potential, then the potential function q is actually zero.
基金Supported by the National Natural Science Foundation of China under Grant No.11561050supported by the Natural Science Foundation of Inner Mongolia under Grant No.2016BS0103,2014MS0701the Science and Technology Plan Projects of Inner Mongolia under Grant No.NJZY16141,NJZY16142,NJZY16143
文摘We investigate a class of fourth-order regular differential operator with transmission conditions at an interior discontinuous point and the eigenparameter appears not only in the differential equation but also in the boundary conditions. We prove that the operator is symmetric, construct basic solutions of differential equation, and give the corresponding Green function of the operator is given.
