We prove the existence of orbitally stable standing waves with prescribed L2-norm for the following Schrödinger-Poisson type equation in ℝ when p = {8/3} ∪(3, 10/3).In the case 3 < p < 10/3, we prove the existence and stability only for sufficiently large L2-norm. In case p = 8/3, our approach recovers the result of Sanchez and Soler (J Stat Phys 114:179-204, 2004) for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In the final section, a further application to the Schrödinger equation involving the biharmonic operator is given. © 2010 Springer Basel AG.
Stable standing waves for a class of nonlinear Schrödinger-Poisson equations
Siciliano G.
2011-01-01
Abstract
We prove the existence of orbitally stable standing waves with prescribed L2-norm for the following Schrödinger-Poisson type equation in ℝ when p = {8/3} ∪(3, 10/3).In the case 3 < p < 10/3, we prove the existence and stability only for sufficiently large L2-norm. In case p = 8/3, our approach recovers the result of Sanchez and Soler (J Stat Phys 114:179-204, 2004) for sufficiently small charges. The main point is the analysis of the compactness of minimizing sequences for the related constrained minimization problem. In the final section, a further application to the Schrödinger equation involving the biharmonic operator is given. © 2010 Springer Basel AG.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
