ON THE LOGARITHMIC SCHRÖDINGER EQUATION
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- 21 April 2014
- journal article
- Published by World Scientific Pub Co Pte Ltd in Communications in Contemporary Mathematics
- Vol. 16 (2)
- https://doi.org/10.1142/s0219199713500326
Abstract
In the framework of the nonsmooth critical point theory for lower semi-continuous functionals, we propose a direct variational approach to investigate the existence of infinitely many weak solutions for a class of semi-linear elliptic equations with logarithmic nonlinearity arising in physically relevant situations. Furthermore, we prove that there exists a unique positive solution which is radially symmetric and nondegenerate.Keywords
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This publication has 25 references indexed in Scilit:
- Symmetry and monotonicity of least energy solutionsCalculus of Variations and Partial Differential Equations, 2009
- Spectra of Linearized Operators for NLS Solitary WavesSIAM Journal on Mathematical Analysis, 2008
- Soliton dynamics in a potentialMathematical Research Letters, 2000
- Subdifferential Calculus and Nonsmooth Critical Point TheorySIAM Journal on Optimization, 2000
- The Schrödinger EquationPublished by Springer Science and Business Media LLC ,1991
- Stable solutions of the logarithmic Schrödinger equationNonlinear Analysis, 1983
- Orbital stability of standing waves for some nonlinear Schr dinger equationsCommunications in Mathematical Physics, 1982
- Équations d'évolution avec non linéarité logarithmiqueAnnales de la Faculté des sciences de Toulouse : Mathématiques, 1980
- Gaussons: Solitons of the Logarithmic Schrödinger EquationPhysica Scripta, 1979
- Nonlinear wave mechanicsAnnals of Physics, 1976