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Ukrainian Mathematical Journal

, Volume 50, Issue 11, pp 1796–1800 | Cite as

Riquier problem for a nonlinear equation resolved with respect to the iterated Levi Laplacian

  • M. N. Feller
Brief Communications

Abstract

Solutions are found for the nonlinear equation Δ L 2 U(x) = f(U(x)) (here, Δ L is an infinite-dimensional Laplacian) which is solved with respect to the iterated infinite-dimensional Laplacian. The Riquier problems are stated for an equation of this sort.

Keywords

Hilbert Space Harmonic Function Nonlinear Equation Elliptic Equation Orthonormal Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    P. Levi, Concrete Problems of Function Analysis [in Russian], Nauka, Moscow (1967).Google Scholar
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    E. M. Polishchuk, “Linear equations in functional Laplacian operators,” Usp. Mat. Nauk, 19, No. 2, 163–170 (1964).zbMATHGoogle Scholar
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    G. E. Shilov, “On some problems of analysis in the Hilbert space. III,” Ate. Sb., 74 (116), No. 1, 161–168 (1967).Google Scholar
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    M. N. Feller, “On polyharmonic equation in a functional space,” Dokl. Akad. Nauk Ukr.SSR, Ser A, No. 11, 1005–1011 (1968).Google Scholar
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    M. N. Feller, “Infinite-dimensional elliptic equations and operators of the Levi type,” Usp. Mat. Nauk, 41, No. 4, 97–140 (1986).MathSciNetGoogle Scholar

Copyright information

© Kluwer Academic/Plenum Publishers 1998

Authors and Affiliations

  • M. N. Feller
    • 1
  1. 1.UkrNIIMODKiev

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