Solvability of some integro-differential equations with drift

Abstract

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.