Applied Mathematics & Information Sciences

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In this work a Sturm-Liouville operator with discontinuous coefficient and a spectral parameter in boundary conditions is considered. The orthogonality of the eigenfunctions, realness and simplicity of the eigenvalues are investigated. It is shown that the eigenfunctions form a complete system and expansion formula with respect to eigenfunctions is obtained. Also, the evolution of the Weyl solution andWeyl function is discussed. Uniqueness theorem for the solution of the inverse problem withWeyl function is proved.