On Spectral Properties of Discontinuous Differential Operator with Second Order

Abstract

In this work, we consider the spectral problem for a second-order discontinuous differential operator with a spectral parameter in the boundary condition in $L_p, 1<p<\infty$. We study a method for establishing the basicity of eigenfunctions for such a problem. Such spectral problems arise while one solves the problem of a loaded string fixed at both ends with a load placed in the between ends of the string by the Fourier method.