Cazenave, Thierry Stable solutions of the logarithmic Schrödinger equation. (English) Zbl 0529.35068 Nonlinear Anal., Theory Methods Appl. 7, 1127-1140 (1983). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 56 Documents 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 Keywords:logarithmic Schrödinger equation; orbital stability; stationary states; Cauchy problem; well-posed Citations:Zbl 0513.35007 PDF BibTeX XML Cite \textit{T. Cazenave}, Nonlinear Anal., Theory Methods Appl. 7, 1127--1140 (1983; Zbl 0529.35068) Full Text: DOI OpenURL 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.