The nonlinear Schrodinger equation has received a great deal of attention from
mathematicians, particularly because of its applications to nonlinear optics. It is also a good …

The purpose of this note is to give a survey of some recent work on dispersive estimates for
the Schrödinger flow eitHP c, H=−△+ V on Rd, d≥ 1,(12.1) where Pc is the projection onto …

We prove Strichartz estimates for the Schrödinger equation with an electromagnetic
potential, in dimension n⩾ 3. The decay and regularity assumptions on the potentials are …

We characterize the radial functionsVin R nfor which the a priori inequality‖∇ u1/2‖ 2+
k‖ uV1/2‖ 2⩽ C‖ V− 1/2 (Δ+ k2) u‖ 2holds with constant independent ofk. The condition …

У нлгж з в д ж з з з в йа ж ви ж а гд ж игжИ б м б а гд ж игжИ аг а Хгжж нЙинд зд зИ Р ж н
гд ж игж гв и гв г бгвгигв йв и гвзИ л Хгжж нЙинд зд зИ л и зи б и зК Х и б и з Ый и а зз и гв …

We obtain mapping estimates for the Schrödinger resolvent (-Δ+V-λ^2)^-1 in R 3, where the
potential is assumed to satisfy only an integrability condition. No pointwise decay or …

Mathematische Annalen Page 1 DOI: 10.1007/s00208-003-0444-7 Math. Ann. 328, 1–25 (2004)
Mathematische Annalen Non trivial Lq solutions to the Ginzburg-Landau equation Susana …

In this paper, the authors give a characterization of the (L p, λ, L q, λ)-compactness for the
Riesz potential commutator b, I α. More precisely, the authors prove that the commutator b, I …

We prove asymptotic completeness for operators of the form H=-Δ+ L on L 2 (R d), d≥ 2,
where L is an admissible perturbation. Our class of admissible perturbations contains …

We consider asymptotic stability of a small solitary wave to supercritical $1 $-dimensional
nonlinear Schrödinger equations\[iu_t+ u_ {xx}= Vu\pm| u|^{p-1} u\quad\text {for}(x …