Abstract
We present a method of solving for the nonlinear equationf(U(x),Δ 2 L U(x)) = Δ L U(x) (Δ L is an infinite-dimensional Laplacian) unresolved with respect to an iterated infinite-dimensional Laplacian and for the Riquier problem for this equation.
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References
P. Lévy,Problèmes Concrets d’Analyse Fonctionnelle, Paris (1951).
M. N. Feller, “On a nonlinear equation unsolved with respect to the Lévy Laplacian,”Ukr. Mat. Zh.,48, No. 5, 719–721 (1996).
M. N. Feller, “The Riquier problem for a nonlinear equation resolved with respect to the Lévy iterated Laplacian,”Ukr. Mat. Zh.,50, No. 11, 1574–1577 (1998).
M. N. Feller, “Infinite-dimensional elliptic equations and operators of Lévy’s type,”Usp. Mat. Nauk,41, No. 4, 97–140 (1986).
Additional information
Ukrainian NII MOD, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 3, pp. 423–427, March, 1999.
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Feller, M.N. The riquier problem for a nonlinear equation unresolved with respect to the Lévy iterated laplacian. Ukr Math J 51, 470–475 (1999). https://doi.org/10.1007/BF02592485
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DOI: https://doi.org/10.1007/BF02592485