We investigate the existence of ground states for the focusing Nonlinear Schroedinger Equation on the infinite three-dimensional cubic grid. We extend the result found for the analogous two-dimensional grid by proving an appropriate Sobolev inequality giving rise to a family of critical Gagliardo-Nirenberg inequalities that hold for every nonlinearity power from 10/3 to 6, namely, from the L^2-critical power for the same problem in R^3 to the critical power for the same problem in R. Given the Gagliardo-Nirenberg inequality, the problem of the existence of ground states can be treated as already done for the two-dimensional grid.
One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid / Adami, Riccardo; Dovetta, Simone. - In: RENDICONTI DI MATEMATICA E DELLE SUE APPLICAZIONI. - ISSN 1120-7183. - 39:7(2018), pp. 181-194.
|Titolo:||One-dimensional versions of three-dimensional system: Ground states for the NLS on the spatial grid|
|Data di pubblicazione:||2018|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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