Elliptic spectral problems of higher order with eigenparameter dependent boundary conditions

Let A be a uniformly elliptic differential operator of order 2m on a smooth bounded domain Omega subset of R-n. We consider the spectral problem Au = lambdau subject to boundary conditions B(0)u = lambdaB(1)u, B ' (1)u = 0, where B-0, B-1, and B ' (1) are sets of boundary operators. The problem is recast in the form Au = lambdau in an appropriate Hilbert space, and the essential spectrum of the corresponding operator A is found.