Abstract:
Series of asymptotic solutions of nonlinear elliptic boundary-value problems in compact domains with a spectral parameter contained in the boundary condition are constructed, and the connection of these solutions with the trajectories of classical Hamiltonian systems defined on the boundary of the domains considered is established. The asymptotic solutions indicated are expressed in terms of multidimensional Dirichlet series, and a superposition law is established for them which, as it turns out, does not depend either on the number of independent variables in the original problem or on the form of the nonlinearity.
Citation:
S. Yu. Dobrokhotov, V. P. Maslov, “Multidimensional Dirichlet series in the problem of the asymptotic behavior of spectral series of nonlinear elliptic operators”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat., 23, VINITI, Moscow, 1983, 137–222; J. Soviet Math., 28:1 (1985), 91–143
\Bibitem{DobMas83}
\by S.~Yu.~Dobrokhotov, V.~P.~Maslov
\paper Multidimensional Dirichlet series in the problem of the asymptotic behavior of spectral series of nonlinear elliptic operators
\serial Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat.
\yr 1983
\vol 23
\pages 137--222
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/intd70}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=734315}
\zmath{https://zbmath.org/?q=an:0564.58035}
\transl
\jour J. Soviet Math.
\yr 1985
\vol 28
\issue 1
\pages 91--143
\crossref{https://doi.org/10.1007/BF02104897}
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https://www.mathnet.ru/eng/intd/v23/p137
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