Half-inverse problems for the quadratic pencil of the Sturm–Liouville equations with impulse

Abstract

In this paper, we consider the inverse spectral problem for the impulsive Sturm–Liouville differential pencils on [0, π] with the Robin boundary conditions and the jump conditions at the point 𝜋������ 2 . We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials given on ( 0, 𝜋������ 2 ) . and (ii) the potentials given on ( 𝜋������ 2 , 𝜋������ ) , where 0<α<1, respectively. Inverse spectral problems, Sturm–Liouville operator, spectrum, uniqueness.