TY - JOUR
T1 - Minimization of the lowest eigenvalue for a vibrating beam
AU - Liang, Quanyi
AU - Liu, Kairong
AU - Meng, Gang
AU - She, Zhikun
PY - 2018/4
Y1 - 2018/4
N2 - In this paper we solve the minimization problem of the lowest eigenvalue for a vibrating beam. Firstly, based on the variational method, we establish the basic theory of the lowest eigenvalue for the fourth order measure differential equation (MDE). Secondly, we build the relationship between the minimization problem of the lowest eigenvalue for the ODE and the one for the MDE. Finally, with the help of this built relationship, we find the explicit optimal bound of the lowest eigenvalue for a vibrating beam.
AB - In this paper we solve the minimization problem of the lowest eigenvalue for a vibrating beam. Firstly, based on the variational method, we establish the basic theory of the lowest eigenvalue for the fourth order measure differential equation (MDE). Secondly, we build the relationship between the minimization problem of the lowest eigenvalue for the ODE and the one for the MDE. Finally, with the help of this built relationship, we find the explicit optimal bound of the lowest eigenvalue for a vibrating beam.
KW - Eigenvalue
KW - Minimization problem
KW - The fourth order equation
UR - https://www.scopus.com/pages/publications/85041082479
U2 - 10.3934/dcds.2018085
DO - 10.3934/dcds.2018085
M3 - 文章
AN - SCOPUS:85041082479
SN - 1078-0947
VL - 38
SP - 2079
EP - 2092
JO - Discrete and Continuous Dynamical Systems- Series A
JF - Discrete and Continuous Dynamical Systems- Series A
IS - 4
ER -