Abstract
An existence theorem for a certain class of nonlinear nonlocal Schroedinger operators is presented and the sketch of the proof is given. In addition, it is shown that there exist soliton-like solutions for nonlinear nonlocal systems describing generalized dynamics of an inhomogeneous electron gas in a crystal.
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References
S. Lundquist, N.H. March, eds.Theory of Inhomogeneous Electron Gas, Plenum Press, New York-London 1983.
P.Hohenberg, W.Kohn, Phys.Rev.B 136, 864–871 (1964).
E.H.Lieb, Intern.J.Quant.Chem. 24, 243–277 (1983).
V.P.Maslov, Contemporary Problems of Mathematics 11, 153–234 (1978) (in Russian).
M.Reed, B.Simon, Methods of Modern Mathematical Physics, vol.4, Academic Press, New York 1978.
S.I.Petrukhnovsky,Preprint No 84/3, Institute of Metal Physics, Ural Scientific Centre of the Soviet Academy of Sciences, Sverdlovsk 1984 (in Russian).
J.Schauder, Math.Zetschr. 26, 47–65 (1927).
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© 1990 Birkhäuser Verlag Basel
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Petrukhnovsky, S.I. (1990). An Existence Theorem for Some Nonlinear Nonlocal Schroedinger Operators and the Soliton-Like Solutions for the Corresponding Dynamic Systems. In: Exner, P., Neidhardt, H. (eds) Order,Disorder and Chaos in Quantum Systems. Operator Theory: Advances and Applications, vol 46. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-7306-2_32
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DOI: https://doi.org/10.1007/978-3-0348-7306-2_32
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-0348-7308-6
Online ISBN: 978-3-0348-7306-2
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