Journal
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
Volume 222, Issue 3, Pages 1581-1600Publisher
SPRINGER
DOI: 10.1007/s00205-016-1028-5
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We prove the uniqueness of positive ground state solutions of the problem , , and as . This equation is derived from the logarithmic Schrodinger equation , and also from the classical equation . For each , a positive ground state solution is . We combine with energy estimates and associated Ricatti equation estimates to prove that, for each , is the only positive ground state. We also investigate the stability of . Several open problems are stated.
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