We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation wi...We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue problem. We investigate the representation of the four Sturm-Liouville operators by infinite banded matrices.展开更多
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
The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreove...The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreover, we examine the properties of the kernel function of this integral representation and obtain the partial differential equation provided by this kernel function.展开更多
This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas fo...This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.展开更多
The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such op...The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.展开更多
Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge fiel...Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.展开更多
Abstract In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm Liouville boundary value problems for nonlinear second order impulsive differential equations in Banach spa...Abstract In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm Liouville boundary value problems for nonlinear second order impulsive differential equations in Banach spaces.展开更多
By using the upper and lower solutions method and fixed point theory,we investigate a class of fourth-order singular differential equations with the Sturm-Liouville Boundary conditions.Some sufficient conditions are o...By using the upper and lower solutions method and fixed point theory,we investigate a class of fourth-order singular differential equations with the Sturm-Liouville Boundary conditions.Some sufficient conditions are obtained for the existence of C2[0,1] positive solutions and C3[0,1] positive solutions.展开更多
文摘We investigate the Hill differential equation ?where A(t), B(t), and D(t) are trigonometric polynomials. We are interested in solutions that are even or odd, and have period π or semi-period π. The above equation with one of the above conditions constitutes a regular Sturm-Liouville eigenvalue problem. We investigate the representation of the four Sturm-Liouville operators by infinite banded matrices.
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 Scientific and Technological Research Council of Turkey(TüBìTAK)
文摘The aim of this paper is to construct the integral representation of the solution of Sturm-Liouville equation with eigenparameter-dependent discontinuity conditions at an interior point of the finite interval. Moreover, we examine the properties of the kernel function of this integral representation and obtain the partial differential equation provided by this kernel function.
文摘This work studies the asymptotic formulas for the solutions of the Sturm-Liouville equation with the polynomial dependence in the spectral parameter. Using these asymptotic formulas it is proved some trace formulas for the eigenvalues of a simple boundary problem generated in a finite interval by the considered Sturm-Liouville equation.
文摘The boundary value problem with a spectral parameter in the boundary conditions for a polynomial pencil of the Sturm-Liouville operator is investigated. Using the properties of the transformation operators for such operators, the asymptotic formulas for eigenvalues of the boundary value problem are obtained.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10773002,10875012,and 11175019supported by the Fundamental Research Funds for the Central Universities under Grant No. 105116
文摘Using classical time-average approximation, critical temperature and condensed solution in holographic pwave superconductors with a time-dependent source is investigated in probe limit. By choosing suitable gauge field ansatz, the equation of motion for a vector field is presented. With the help of the Sturm-Liouville equation, concrete values of phase transition temperature and criticaJ frequency are obtained. It is shown that the phase transition temperature enhances as the frequency of the time-dependent source raises in high frequency regime, which means that the operators on the boundary field theory will be easier to condense.
文摘Abstract In this paper, the fixed point theorem is applied to investigate the existence of solutions of Sturm Liouville boundary value problems for nonlinear second order impulsive differential equations in Banach spaces.
基金Research supported by the National Natural Science Foundation of China(10471075)the Natural Science Foun-dation of Shandong Province of China(Y2006A04)
文摘By using the upper and lower solutions method and fixed point theory,we investigate a class of fourth-order singular differential equations with the Sturm-Liouville Boundary conditions.Some sufficient conditions are obtained for the existence of C2[0,1] positive solutions and C3[0,1] positive solutions.
