19-51 Messoud Efendiev, Vitali Vougalter

On the solvability of some systems of integro-differential equations with drift (270K, pdf) Sep 16, 19

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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 H^2 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 L^1 of the integral kernels implies the existence and convergence in H^2 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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