Abstract
We study degenerate boundary-value problems for higher order ordinary differential
equations with polynomial spectral parameter in both the equation and boundary conditions.
An isomorphism and a coercive solvability of such problems have been established.
We also treat initial boundary-value problems for higher order degenerate parabolic equations.
Both studies include, in particular, second order equations with the general Wentzell boundary
conditions. Moreover, the equation may contain a linear abstract operator and boundary conditions
may contain linear functionals and values of an unknown functions and its derivatives
in some inside points of the interval of the problem.
