Mixed problems with non-homogeneous boundary conditions in Lipschitz domains for second-order elliptic equations with a parameter

For a second-order elliptic equation involving a parameter, with principal part in divergence form in a Lipschitz domain Omega mixed problems (of Zaremba type) with non-homogeneous boundary conditions are considered for generalized functions in W-2(1)(Omega). The poincare-Steklov operators on a Lipschitz piece gamma of the domain's boundary Gamma corresponding to homogeneous mixed boundary conditions on Gamma \ gamma are studied. For a homogeneous equation with separation of variables in a tube domain with Lipschitz section, the Fourier method is substantiated for homogeneous mixed boundary conditions on the lateral surface and non-homogeneous conditions on the ends.