In this work, we discuss the inverse problem for the impulsive differential pencil with eigenparameter dependent boundary conditions on \((0, \pi )\) . We prove two uniqueness theorems by the interior inverse problem and the Weyl function technique. Taking the Weyl function technique, we show that if coefficients of the first boundary condition, i.e. \(h_{1}, h_{2}\) are known, then the potentials \(p(x),\ q(x)\) and the coefficients of the second boundary condition, i.e. \(H_{1}, H_{2},\) are uniquely determined by information about the eigenfunctions at the midpoint of the interval and one spectrum or partial information on the eigenfunctions at some internal points and some of two spectra.
