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.