Inverse Problems for the Quadratic Pencil of the Sturm-Liouville Equations with Impulse

Rauf Kh. Amırov, A. Adiloglu Nabıev
2013 Abstract and Applied Analysis  
In this study some inverse problems for a boundary value problem generated with a quadratic pencil of Sturm-Liouville equations with impulse on a finite interval are considered. Some useful integral representations for the linearly independent solutions of a quadratic pencil of Sturm-Liouville equation have been derived and using these, important spectral properties of the boundary value problem are investigated; the asymptotic formulas for eigenvalues, eigenfunctions, and normalizing numbers
more » ... rmalizing numbers are obtained. The uniqueness theorems for the inverse problems of reconstruction of the boundary value problem from the Weyl function, from the spectral data, and from two spectra are proved.
doi:10.1155/2013/361989 fatcat:4i475b4cyfeb3k2xsg774fw2hi