This paper studies the eigenvalue problem for p（x）-Laplacian equations involving Robin boundary condition. We obtain the Euler-Lagrange equation for the minimization of the Rayleigh quotient involving Luxemburg norm...This paper studies the eigenvalue problem for p（x）-Laplacian equations involving Robin boundary condition. We obtain the Euler-Lagrange equation for the minimization of the Rayleigh quotient involving Luxemburg norms in the framework of variable exponent Sobolev space. Using the Ljusternik-Schnirelman principle, for the Robin boundary value problem, we prove the existence of infinitely many eigenvalue sequences and also show that, the smallest eigenvalue exists and is strictly positive, and all eigenfunctions associated with the smallest eigenvalue do not change sign.展开更多
The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytica...The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.展开更多
Based on coupled-mode theo ry , the eigenvalue equation of five-layered long-period fiber grating(LPFG) sens or with Ag film and gas-sensitive film overlays are firstly studied. The probl em of resolving complex eigen...Based on coupled-mode theo ry , the eigenvalue equation of five-layered long-period fiber grating(LPFG) sens or with Ag film and gas-sensitive film overlays are firstly studied. The probl em of resolving complex eigenvalue equation on five-layered LPFG is analyzed, a nd the method of resolution is also given. Then the eigenvalue equation of three -layered metal cladding LPFG is analyzed, and the complex transcendental equati on is also discussed. The computing result shows that the coupling between the l ow-order EH modes and the core mode is much stronger than that between the low -order HE modes and the core mode.展开更多
We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）met...We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）method.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11571057)
文摘This paper studies the eigenvalue problem for p（x）-Laplacian equations involving Robin boundary condition. We obtain the Euler-Lagrange equation for the minimization of the Rayleigh quotient involving Luxemburg norms in the framework of variable exponent Sobolev space. Using the Ljusternik-Schnirelman principle, for the Robin boundary value problem, we prove the existence of infinitely many eigenvalue sequences and also show that, the smallest eigenvalue exists and is strictly positive, and all eigenfunctions associated with the smallest eigenvalue do not change sign.
基金supported by the National Natural Science Foundation of China(12172023).
文摘The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.
基金"Shu Guang"Plan of Education Committee of Shanghai (02SG32) Natural Science Foundation of ScienceCommittee of Shanghai(03ZR14071)
文摘Based on coupled-mode theo ry , the eigenvalue equation of five-layered long-period fiber grating(LPFG) sens or with Ag film and gas-sensitive film overlays are firstly studied. The probl em of resolving complex eigenvalue equation on five-layered LPFG is analyzed, a nd the method of resolution is also given. Then the eigenvalue equation of three -layered metal cladding LPFG is analyzed, and the complex transcendental equati on is also discussed. The computing result shows that the coupling between the l ow-order EH modes and the core mode is much stronger than that between the low -order HE modes and the core mode.
文摘We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）method.
