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Usted está aquí: Inicio / Actividades / Seminarios / Seminario de Ecuaciones Diferenciales No Lineales (SEDNOL) / Actividades del Seminario de Ecuaciones Diferenciales No Lineales / Ground states for the interface of two periodic media and other irregular Schrödinger equations

Ground states for the interface of two periodic media and other irregular Schrödinger equations

Ponente: Julián Chagoya
Institución: IMUNAM
Tipo de Evento: Investigación
Cuándo 01/12/2016
de 11:00 a 12:00
Dónde Salón 1
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Resumen:

We consider the stationary semilinear Schrödinger equation

-Δu+V(x)u=a(x)|u|^{p-2}u, u∈H¹(R^{N}),

where 2<p<2^{∗} (2^{∗}=2N/(N-2) for N≥3 , 2^{∗}=∞ for N=2) and a,V∈L^{∞}(R^{N}), infV>0. In our previous work we have proved a variation of the Splitting Lemma that is valid even when the functions V and a do not have a limit at infinity, so there is not a limit problem in the usual sense. Now we present how this result can be applied when V takes the values of two different periodic functions over disjoints domains whose union is R^{N}, and something similar happens with a. We will also analyze conditions that assure an inequality between energy levels involved in the Splitting Lemma, that had been given in this and other irregular problems.