The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity

Riccardo Adami; Gianfausto Dell'Antonio; Rodolfo Figari; Alessandro Teta

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 3, page 477-500
  • ISSN: 0294-1449

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Adami, Riccardo, et al. "The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity." Annales de l'I.H.P. Analyse non linéaire 20.3 (2003): 477-500. <http://eudml.org/doc/78587>.

@article{Adami2003,
author = {Adami, Riccardo, Dell'Antonio, Gianfausto, Figari, Rodolfo, Teta, Alessandro},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {3D nonlinear Schrödinger equation; point interactions; nonlinear Dirac delta potentials; existence and uniqueness in energy space; Cauchy problem},
language = {eng},
number = {3},
pages = {477-500},
publisher = {Elsevier},
title = {The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity},
url = {http://eudml.org/doc/78587},
volume = {20},
year = {2003},
}

TY - JOUR
AU - Adami, Riccardo
AU - Dell'Antonio, Gianfausto
AU - Figari, Rodolfo
AU - Teta, Alessandro
TI - The Cauchy problem for the Schrödinger equation in dimension three with concentrated nonlinearity
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2003
PB - Elsevier
VL - 20
IS - 3
SP - 477
EP - 500
LA - eng
KW - 3D nonlinear Schrödinger equation; point interactions; nonlinear Dirac delta potentials; existence and uniqueness in energy space; Cauchy problem
UR - http://eudml.org/doc/78587
ER -

References

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  2. [2] Adami R., Teta A., A class of nonlinear Schrödinger equation with concentrated nonlinearity, J. Funct. Anal.180 (2001) 148-175. Zbl0979.35130MR1814425
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  7. [7] Erdely A. et al. , Tables of Integral Transform, McGraw-Hill, New York, 1954. 
  8. [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. Zbl0396.35028MR533218
  9. [9] Gorenflo R., Vessella S., Abel Integral Equations, Springer-Verlag, Berlin, 1978. Zbl0717.45002MR1095269
  10. [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. Zbl0635.45017MR906804
  11. [11] Kato T., On nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Physique Théorique46 (1987) 113-129. Zbl0632.35038MR877998
  12. [12] Miller R.K., Nonlinear Volterra Integral Equations, W.A. Benjamin, 1971. Zbl0448.45004MR511193
  13. [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. Zbl0599.35035MR720214
  14. [14] Teta A., Quadratic forms for singular perturbations of the Laplacian, Publ. R.I.M.S. Kyoto Univ.26 (1990) 803-817. Zbl0735.35048MR1082317
  15. [15] Weinstein M.I., NLSE and sharp interpolation estimates, Comm. Math. Phys.87 (1982/83) 567-576. Zbl0527.35023MR691044

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