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A logarithmic Schrödinger equation with periodic potential

Ponente: Andrzej Szulkin
Institución: Universidad de Estocolmo
Cuándo 23/10/2014
de 11:00 a 12:00
Dónde Salón de seminarios Graciela Salicrup
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We consider the logarithmic Schrödinger equation
\begin{equation*}
-\Delta u + V(x)u = Q(x)u\log u^2, \quad u\in H^1(\mathbb{R}^N),
\end{equation*}
where \(V,Q\) are periodic in \(x_1,\ldots,x_N\), \(Q>0\) and \(V+Q>0\). We show that this equation has
infinitely many geometrically distinct solutions and that one of these solutions is positive. The main
difficulty here is that the functional associated with this problem is lower semicontinuous and takes
the value \(+\infty\) for some \(u\in H^1(\mathbb{R}^N)\).
This is joint work with Marco Squassina.