Abstract
We establish the existence in the sense of sequences of solutions for certain systems of integro-differential equations involving the drift terms in the appropriate H2 spaces by means of the fixed point technique when the elliptic problems contain second order differential operators with and without Fredholm property. It is proven that, under the reasonable technical conditions, the convergence in L1 of the integral kernels implies the existence and convergence in H2 of the solutions. We emphasize that the study of the system case is more difficult than of the scalar case and requires to overcome more cumbersome technicalities.
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