RT Journal Article
SR 00
A1 Bégout, Pascal
A1 Diaz, Jesus Ildefonso
T1 On a nonlinear Schrödinger equation with a localizing effect
JF Comptes rendus. Mathematique
YR 2006
FD 2006
VO 342
IS 7
SP 459
OP 463
AB We consider the nonlinear Schrödinger equation associated to a singular potential of the form   $a|u|^{-(1-m)}u+bu,$ for some $m\in(0,1),$ on a possible unbounded domain. We use some suitable energy methods to prove that if $\mathrm{Re}(a)+\mathrm{Im}(a)>0$ and if the initial and right hand side data have compact support then any possible solution must also have a compact support for any $t>0.$ This property contrasts with the behavior of solutions associated to regular potentials $(m\ge1).$ Related results are proved also for the associated stationary problem and for self-similar solution on the whole space and potential $a|u|^{-(1-m)}u.$ The existence of solutions is obtained by some compactness methods under additional conditions.
PB Elsevier
SN 1631-073X
LK https://publications.ut-capitole.fr/id/eprint/35021/