Riquier problem for a nonlinear equation resolved with respect to the iterated Levi Laplacian
- 26 Downloads
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.
KeywordsHilbert Space Harmonic Function Nonlinear Equation Elliptic Equation Orthonormal Basis
Unable to display preview. Download preview PDF.
- 1.P. Levi, Concrete Problems of Function Analysis [in Russian], Nauka, Moscow (1967).Google Scholar
- 3.G. E. Shilov, “On some problems of analysis in the Hilbert space. III,” Ate. Sb., 74 (116), No. 1, 161–168 (1967).Google Scholar
- 4.M. N. Feller, “On polyharmonic equation in a functional space,” Dokl. Akad. Nauk Ukr.SSR, Ser A, No. 11, 1005–1011 (1968).Google Scholar