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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Efendiev, M., Vougalter, V. (2022). On the Solvability of Some Systems of Integro-Differential Equations with Drift. In: Volchenkov, D., Tenreiro Machado, J.A. (eds) Mathematical Methods in Modern Complexity Science. Nonlinear Systems and Complexity, vol 33. Springer, Cham. https://doi.org/10.1007/978-3-030-79412-5_8
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