Asymptotics of the spectrum of linear operator pencils

The problem $Au=tBu$ is considered in a bounded Lipschitz domain, where $A$ and are sums of a pseudodifferential operator satisfying a transmission condition and a singular Green operator, with $A$ elliptic. Under natural conditions the classical formula for the asymptotics of the spectrum is established, with an estimate of the remainder determined by the character of degeneration in ellipticity of the operator $B$.
Bibliography: 18 titles.