2006 Volume 64 Issue 1 Pages 147-162
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.
