The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity
Adami, Riccardo ; Dell'Antonio, Gianfausto ; Figari, Rodolfo ; Teta, Alessandro
Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003), p. 477-500 / Harvested from Numdam
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@article{AIHPC_2003__20_3_477_0,
     author = {Adami, Riccardo and Dell'Antonio, Gianfausto and Figari, Rodolfo and Teta, Alessandro},
     title = {The Cauchy problem for the Schr\"odinger equation in dimension three with concentrated nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {20},
     year = {2003},
     pages = {477-500},
     doi = {10.1016/S0294-1449(02)00022-7},
     mrnumber = {1972871},
     zbl = {1028.35137},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2003__20_3_477_0}
}

Adami, Riccardo; Dell'Antonio, Gianfausto; Figari, Rodolfo; Teta, Alessandro. The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 20 (2003) pp. 477-500. doi : 10.1016/S0294-1449(02)00022-7. http://gdmltest.u-ga.fr/item/AIHPC_2003__20_3_477_0/

[1] Adami R., Teta A., A Simple Model of Concentrated Nonlinearity, Operator Theory: Advances and Applications, 108, 1999, 183-189. | MR 1708796 | Zbl 0967.81010

[2] 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

[3] Adams R., Sobolev Spaces, Academic Press, New York, 1975. | MR 450957 | Zbl 0314.46030

[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, 26, IMUFRJ, Rio de Janeiro, 1993.

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

[7] Erdely A. et al. , Tables of Integral Transform, McGraw-Hill, New York, 1954.

[8] 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

[9] Gorenflo R., Vessella S., Abel Integral Equations, Springer-Verlag, Berlin, 1978. | MR 1095269 | Zbl 0717.45002

[10] Kappel F., Kunisch K., Invariance results for Delay and Volterra equations in fractional order Sobolev spaces, Trans. Math. Soc. 304 (1) (1987) 1-51. | MR 906804 | Zbl 0635.45017

[11] Kato T., On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique 46 (1987) 113-129. | Numdam | MR 877998 | Zbl 0632.35038

[12] Miller R.K., Nonlinear Volterra Integral Equations, W.A. Benjamin, 1971. | MR 511193 | Zbl 0448.45004

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

[14] Teta A., Quadratic forms for singular perturbations of the Laplacian, Publ. R.I.M.S. Kyoto Univ. 26 (1990) 803-817. | MR 1082317 | Zbl 0735.35048

[15] Weinstein M.I., NLSE and sharp interpolation estimates, Comm. Math. Phys. 87 (1982/83) 567-576. | MR 691044 | Zbl 0527.35023