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 On the logarithmic Schrodinger equation

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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.

Author: Pietro d'Avenia; Eugenio Montefusco; Marco Squassina

Source: https://archive.org/

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