Asymptotic distribution of eigenvalues and eigenfunctions for a multi-point discontinuous Sturm-Liouville problem

Abstract

In this article we study a class of generalized BVP' s consisting of discontinuous Sturm-Liouville equation on finite number disjoint intervals, with usual boundary conditions and supplementary transmission conditions at finite number interior points. The asymptotic behaviors of the eigenvalues and eigenfunctions are discussed. By modifying some techniques of classical Sturm-Liouville theory and suggesting own approaches we find asymptotic formulas for the eigenvalues and eigenfunctions.

Keywords

• Sturm-Liouville problems
• eigenvalue
• eigenfunction
• asymptotic distribution