Boundary Value Problems for Elliptic Operator Pencils

In this paper operator pencils A(x,D,$\lambda$) are investigated which depend polynomially on the parameter $\lambda$ and act on a manifold with boundary. The operator A is assumed to satisfy the condition of N-ellipticity with parameter, which is an ellipticity condition, formulated with the use of the Newton polygon. We consider boundary operators B₁(x,D), . . . ,B_m(x.D) of general form and define N-ellipticity for the boundary value problem B₁(x,D), . . . ,B_m(x.D) analogously to the Shapiro-Lopatinskii condition.