Solvability of the abstract Regge boundary value problem and asymptotic behavior of eigenvalues of one abstract spectral problem

In the paper, we give an abstract formulation of the classical Regge boundary value problem (but with a constant potential) in a Ililbert space and prove an isomorphism result for the problem. This result implies, in particular, maximal L_p-regularity for the problem. We also obtain an estimate of the solution with respect to the spectral parameter. Then, for one homogeneous abstract spectral problem, we find asymptotic behavior of its eigenvalues. A possible application of the abstract results to elliptic partial differential equations Is shown at the end of the paper.