In this paper we are concerned with the existence of solutions with non-vanishing angular momentum for a class of nonlinear Schrödinger equations of the form where , , and the potential satisfies some symmetric properties. In particular the cases with radially symmetric and with having a cylindrical symmetry are discussed. Our main purpose is to study the asymptotic behaviour of such solutions in the semiclassical limit (i.e. as ) when a concentration phenomenon around a point of appears.
D'Aprile, T.c. (2002). Some existence and concentration results for nonlinear Schrödinger equations. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 1(4), 457-474 [10.3934/cpaa.2002.1.457].
Some existence and concentration results for nonlinear Schrödinger equations
D'APRILE, TERESA CARMEN
2002-01-01
Abstract
In this paper we are concerned with the existence of solutions with non-vanishing angular momentum for a class of nonlinear Schrödinger equations of the form where , , and the potential satisfies some symmetric properties. In particular the cases with radially symmetric and with having a cylindrical symmetry are discussed. Our main purpose is to study the asymptotic behaviour of such solutions in the semiclassical limit (i.e. as ) when a concentration phenomenon around a point of appears.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
