We investigate systems of differential equations with essentially infinite-dimensional elliptic operators (of the Laplace–Lévy type). For nonlinear systems, we prove theorems on the existence and uniqueness of solutions. For a linear system, we give an explicit formula for the solution.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 63, No. 9, pp. 1257–1262, September, 2011.
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Statkevych, V.M. Systems of essentially infinite-dimensional differential equations. Ukr Math J 63, 1433–1440 (2012). https://doi.org/10.1007/s11253-012-0589-1
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DOI: https://doi.org/10.1007/s11253-012-0589-1