On the logarithmic Schrodinger equation

2013/04/25 by Pietro d'Avenia, Eugenio Montefusco, d'Avenia, Pietro +3 · 2 citations
Mathematics · #35Q40 #35Q41 #35Q51 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35Q40 #msc:35Q41 #msc:35Q51

paper · pdf · doi:10.48550/arxiv.1304.6878

10 pages

arxiv created 2013/05/12 · arxiv updated 2013/05/14

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.

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