@article{Zhang2022, 
author = {Hai-yan Zhang and Ji-jun Ao and Fang-zhen Bo},
title = {Eigenvalues of fourth-order boundary value problems with distributional potentials},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {5},
pages = {7294-7317},
keywords = {fourth-order boundary value problems, distributional potentials, quasi-derivatives, eigenvalues},
url = {https://www.sciopen.com/article/10.3934/math.2022407},
doi = {10.3934/math.2022407},
abstract = {This paper aims to investigate the fourth-order boundary value problems with distributional potentials. We first prove that the operators associated with the problems are self-adjoint and the corresponding eigenvalues are real. Then we obtain that the eigenvalues of the problems depend not only continuously but also smoothly on the parameters of the problems: the boundary conditions, the coefficient functions and the endpoints. Moreover, we find the differential expressions for each parameter.}
}