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arXiv · 1304.6878

On the logarithmic Schrodinger equation

Pietro d'Avenia·Eugenio Montefusco·Marco Squassina
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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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Pietro d'Avenia, Eugenio Montefusco, Marco Squassina. 2013-05-12. On the logarithmic Schrodinger equation. https://arxiv.org/abs/1304.6878

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