  The inverse spectral problem for the second-order differential pencil with
quadratic dependence on the spectral parameter is studied. We obtain sufficient
conditions for the global solvability of the inverse problem, prove its local
solvability and stability. The problem is considered in the general case of
complex-valued pencil coefficients and arbitrary eigenvalue multiplicities.
Studying local solvability and stability, we take the possible splitting of
multiple eigenvalues under a small perturbation of the spectrum into account.
Our approach is constructive. It is based on the reduction of the nonlinear
inverse problem to a linear equation in the Banach space of infinite sequences.
The theoretical results are illustrated by numerical examples.
