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Stable solutions of the logarithmic Schrödinger equation. (English) Zbl 0529.35068


MSC:

35Q99 Partial differential equations of mathematical physics and other areas of application
35B35 Stability in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
35J10 Schrödinger operator, Schrödinger equation
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics

Citations:

Zbl 0513.35007
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References:

[1] A{\scDAMS} R.A. & C{\scLARKE} F.H., Gross’s Logarithmic Sobolev inequality: a simple proof, preprint.
[2] Berestycki, H.; Lions, P.L., Nonlinear scalar fields equations, Archs ration. mech. analysis, (1980) · Zbl 0707.35143
[3] Bialynicki-Birula, I.; Mycielski, J., Nonlinear wave mechanics, Ann. phys., 100, 62-93, (1976)
[4] Cazenave, T., Equations de Schrödinger non lineaires en dimension deux, Proc. R. soc. edinb., 84, 327-346, (1979) · Zbl 0428.35021
[5] Cazenave, T.; Haraux, A., Equations d’évolution avec non linéarité logarithmique, Annls fac. sci. univ. Toulouse, 2, 21-55, (1980) · Zbl 0411.35051
[6] Ginibre, J.; Velo, G., On a class of nonlinear Schrödinger equations, J. funct. analysis, 32, 1-71, (1979) · Zbl 0396.35029
[7] Kranosel’skii, M.A.; Rutickii, Ya.B., Convex-functions and Orlicz spaces, (1961), Noordhoff Groningen, Netherlands
[8] Lin, J.E.; Strauss, W.A., Decay and scattering of solutions of a nonlinear Schrödinger equation, J. funct. analysis, 30, 245-263, (1978) · Zbl 0395.35070
[9] Reed, M.; Simon, B., Methods of modern mathematical physics, II, (1975), Academic Press New York · Zbl 0308.47002
[10] Strauss, W.A., Existence of solitary waves in higher dimensions, Communs math. phys., 55, 149-162, (1977) · Zbl 0356.35028
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