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 Schrodinger Equation / Pietro, D'Avenia; Montefusco, Eugenio; Marco, Squassina. - In: COMMUNICATIONS IN CONTEMPORARY MATHEMATICS. - ISSN 0219-1997. - STAMPA. - 16:2(2014), pp. 1-15. [10.1142/s0219199713500326]
On the Logarithmic Schrodinger Equation
MONTEFUSCO, Eugenio;
2014
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.