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.

Keywords

• spectral problem,eigenfucntions,completeness,minimality

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