TY  - JOUR
ID  - publications35021
UR  - https://publications.ut-capitole.fr/id/eprint/35021/
IS  - 7
A1  - Bégout, Pascal
A1  - Diaz, Jesus Ildefonso
Y1  - 2006///
N2  - 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
JF  - Comptes rendus. Mathematique
VL  - 342
SN  - 1631-073X
TI  - On a nonlinear Schrödinger equation with a localizing effect
SP  - 459
AV  - public
EP  - 463
ER  -