Spectral Data Asymptotics for Fourth-Order Boundary Value Problems

Abstract

In this paper, we derive sharp asymptotics for the spectral data (eigenvalues and weight numbers) of the fourth-order linear differential equation with a distribution coefficient and three types of separated boundary conditions. Our methods rely on the recent results concerning regularization and asymptotic analysis for higher-order differential operators with distribution coefficients. The results of this paper have applications to the theory of inverse spectral problems as well as a separate significance.

Keywords

• fourth-order differential operators
• distribution coefficients
• eigenvalue asymptotics
• weight numbers