Rayleigh Waves for Elliptic Systems in Domains with Periodic Boundaries

We consider formally self-adjoint elliptic systems of partial differential equations generating formally positive operators and having the polynomial property. Sufficient conditions that ensure the existence of Rayleigh surface waves in the Neumann problem on a half-space with periodic boundary are found. We give examples of specific problems of mathematical physics in which our sufficient conditions are simplified or turn into a criterion and study problems in the theory of plates and piezoelectrics that are not covered by general results. The latter problem requires a major modification of the approach.