On the minimum eigenvalue gap for vibrating string
Copyright policy )On the minimum eigenvalue gap for vibrating string
Consider a Sturm-Liouville problem with Dirichlet type boundary conditions (BCs). To speak more precise consider the differential equation \[ y'' +\lambda \rho(x) y=0 \] with BCs \[ y(0)=y(1)=0. \] As we know \(\rho(x)\) is called the density function and describes the mass distribution of a string. There are mainly two important eigenvalue problems related with successive eigenvalues of this problem: Eigenvalue gap problem and eigenvalue ratio problem. In this paper, following [\textit{J. Qi} et al., Qual. Theory Dyn. Syst. 19, No. 1, Paper No. 12, 15 p. (2020; Zbl 1456.34022)], the author deals with the minimum eigenvalue gap of the first two eigenvalues for \(\rho(x)\), where \(\rho(x)\) is piecewise continuous with a bounded of jumps. Contrary to previous works in the literature, in this paper, the author considers a more general case of this density function.
- Central South University China (People's Republic of)
vibrating string, eigenvalue gap, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Boundary eigenvalue problems for ordinary differential equations, extremal density function
vibrating string, eigenvalue gap, Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators, Boundary eigenvalue problems for ordinary differential equations, extremal density function
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