Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity
Adami, Riccardo ; Dell'Antonio, Gianfausto ; Figari, Rodolfo ; Teta, Alessandro
Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004), p. 121-137 / Harvested from Numdam
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@article{AIHPC_2004__21_1_121_0,
     author = {Adami, Riccardo and Dell'Antonio, Gianfausto and Figari, Rodolfo and Teta, Alessandro},
     title = {Blow-up solutions for the Schr\"odinger equation in dimension three with a concentrated nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {21},
     year = {2004},
     pages = {121-137},
     doi = {10.1016/j.anihpc.2003.01.002},
     mrnumber = {2037249},
     zbl = {1042.35070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2004__21_1_121_0}
}

Adami, Riccardo; Dell'Antonio, Gianfausto; Figari, Rodolfo; Teta, Alessandro. Blow-up solutions for the Schrödinger equation in dimension three with a concentrated nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 21 (2004) pp. 121-137. doi : 10.1016/j.anihpc.2003.01.002. http://gdmltest.u-ga.fr/item/AIHPC_2004__21_1_121_0/

[1] R. Adami, G. Dell'Antonio, R. Figari, A. Teta, The Cauchy problem for the Schrödinger equation in dimension three with a concentrated nonlinearity, Preprint, Département de mathématiques et applications, École normale supérieure, DMA-02-09, Ann. Inst. H. Poincaré Anal. Non Linéaire, in press. | Numdam | Zbl 1028.35137

[2] Adami R, Teta A, A simple model of concentrated nonlinearity, Operator Theory Adv. Appl. 108 (1999) 183-189. | MR 1708796 | Zbl 0967.81010

[3] Adami R, Teta A, A class of nonlinear Schrödinger equation with concentrated nonlinearity, J. Funct. Anal. 180 (2001) 148-175. | MR 1814425 | Zbl 0979.35130

[4] Albeverio S, Gesztesy F, Högh-Krohn R, Holden H, Solvable Models in Quantum Mechanics, Springer-Verlag, New York, 1988. | MR 926273 | Zbl 0679.46057

[5] Cazenave T, An Introduction to Nonlinear Schrödinger Equation, Textos de Métodos Matematicos, vol. 26, IMUFRJ, Rio de Janeiro, 1993.

[6] Cazenave T, Blow-up and Scattering in the Nonlinear Schrödinger Equation, Textos de Métodos Matematicos, vol. 30, IMUFRJ, Rio de Janeiro, 1996.

[7] Ginibre J, Velo G, On a class of nonlinear Schrödinger equations, I. The Cauchy problem, general case, J. Funct. Anal. 32 (1979) 1-32. | MR 533218 | Zbl 0396.35028

[8] Kato T, On nonlinear Schrödinger equations, Ann. Inst. H. Poincaré Phys. Théor. 46 (1987) 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[9] Merle F, Construction of solutions with exactly k blow-up points for the Schrödinger equation with critical nonlinearity, Comm. Math. Phys. 129 (1990) 223-240. | MR 1048692 | Zbl 0707.35021

[10] Sayapova M.R, Yafaev D.R, The evolution operator for time-dependent potentials of zero radius, Proc. Steklov Inst. Math. 2 (1984) 173-180. | MR 720214 | Zbl 0599.35035

[11] Weinstein M.I, NLSE and sharp interpolation estimates, Comm. Math. Phys. 87 (1983) 567-576. | MR 691044 | Zbl 0527.35023