Periodic and antiperiodic boundary value problems for the Sturm-Liouville equation with the discontinuous coefficient

Abstract

The present paper studies the boundary-value problem in a finite segment generating with the discontinuous Sturm-Liouville equation and periodic(antiperiodic) boundary conditions. We prove completeness of the system of eigenfunctions and generalized eigenfunctions in the space L2(0, π; ρ), obtain the asymptotic formulas for the solution and prove the asymptotic formulas for the eigenvalues of the periodic and antiperiodic boundary value problems