Eigenvalues of the equation \(Au=\lambda Bu\) on a compact manifold without boundary (Q913133)

The authors consider the spectral problem \(Au=\lambda Bu\), \(\lambda\in {\mathbb{C}}\), where A, B are selfadjoint and positive matrix-valued differential operators on a compact manifold without boundary. Under suitable conditions on A and B the spectrum is proved to consist of isolated points \(\lambda_ j\) tending to infinity. The asymptotic behavior of the counting function \(N(\lambda)=\#\{\lambda_ j:\) \(\lambda_ j\leq \lambda \}\) is investigated as well.