Geodesic
On a Class of Nonlinear Schr\"{o}dinger Equations with Nonnegative Potentials in Two Space Dimensions
Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 515-521

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This paper discusses a class of critical nonlinear Schrödinger equations which are closely related to several applications, in particular to Bose-Einstein condensates with attractive two-body interactions. By constructing a constrained variational problem and considering the so-called invariant manifolds of the evolution flow, the authors derive a sharp criterion for blow-up and global existence of the solutions.
Keywords: nonlinear Schrödinger equation, blow-up, nonnegative potentials, constrained variational problem.
Mots-clés : global existence 
@article{MZM_2012_91_4_a3,
     author = {Jian Zhang and Ji Shu},
     title = {On a {Class} of {Nonlinear} {Schr\"{o}dinger} {Equations} with {Nonnegative} {Potentials} in {Two} {Space} {Dimensions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {515--521},
     publisher = {mathdoc},
     volume = {91},
     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a3/}
}
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Jian Zhang; Ji Shu. On a Class of Nonlinear Schr\"{o}dinger Equations with Nonnegative Potentials in Two Space Dimensions. Matematičeskie zametki, Tome 91 (2012) no. 4, pp. 515-521. http://geodesic.mathdoc.fr/item/MZM_2012_91_4_a3/