We prove the existence in the sense of sequences of solutions for some integro-differential
type equations involving the drift term in the appropriate H^2 spaces using the fixed point
technique when the elliptic problems contain second order differential operators with and
without Fredholm property. It is shown that, under the reasonable technical conditions, the
convergence in L^1 of the integral kernels yields the existence and convergence in H^2 of
solutions.

… In this chapter we establish the existence in the sense of sequences of solutions for some
integro-differential type equations containing the drift term and the square root of the one
dimensional negative Laplacian (super-diffusion), on the whole real line or on a finite
interval with periodic boundary conditions in the corresponding H2 spaces. The argument
relies on the fixed point technique when the elliptic equations involve first order differential
operators with and without Fredholm property. It is proven that, under the reasonable …