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
On the logarithmic Schrödinger equation / D'Avenia, Pietro; Montefusco, Eugenio; Squassina, Marco. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 16:2(2014). [10.1142/S0219199713500326]
On the logarithmic Schrödinger equation
D'AVENIA, Pietro;
2014-01-01
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 nondegenerateI documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
