Abstract:
Estimates which depend on the lower bound M of the minimal operator −Δ+q, Imq=0 in the neighborhood of the point x are obtained for the solutions u(x) of the Schrödinger equation. The behavior of u(x) as |x|→∞ in a cone, and in the whole of Rn, is investigated in the case M>0.
Bibliography: 11 titles.
Citation:
Yu. B. Orochko, “On the application of spectral theory to obtain estimates of solutions of the Schrödinger equation”, Math. USSR-Sb., 22:2 (1974), 167–186
\Bibitem{Oro74}
\by Yu.~B.~Orochko
\paper On the application of spectral theory to obtain estimates of solutions of the Schr\"odinger equation
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 2
\pages 167--186
\mathnet{http://mi.mathnet.ru/eng/sm2967}
\crossref{https://doi.org/10.1070/SM1974v022n02ABEH001690}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=344661}
\zmath{https://zbmath.org/?q=an:0285.35019}
Linking options:
https://www.mathnet.ru/eng/sm2967
https://doi.org/10.1070/SM1974v022n02ABEH001690
https://www.mathnet.ru/eng/sm/v135/i2/p170
This publication is cited in the following 3 articles:
D. S. Grebenkov, B.-T. Nguyen, “Geometrical Structure of Laplacian Eigenfunctions”, SIAM Rev, 55:4 (2013), 601
A.L. Delitsyn, B.T. Nguyen, D.S. Grebenkov, “Exponential decay of Laplacian eigenfunctions in domains with branches of variable cross-sectional profiles”, Eur. Phys. J. B, 85:11 (2012)
Yu. B. Orochko, “Carleman estimates for the Schrödinger operator with a locally semibounded strongly singular potential”, Math. USSR-Sb., 33:1 (1977), 147–158
Citation in format AMSBIB
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