Regular and self-similar solutions of nonlinear Schrödinger equations

Journal des Mathematiques Pures et Appliquees

Volumn 77, Issue 10, 1998, Pages 1065-1079

  Ribaud, F ^a   Youssfi, A ^a  

^a UNIVERSITÉ GUSTAVE EIFFEL   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032324914     PISSN: 00217824     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-7824(99)80004-X     Document Type: Article

References (15)

1. [B] G. BOURDAUD, Réalisations des espaces de Besov homogènes. Arkiv Math. 26, 1988, pp. 41-54.
2. [BCG] H. BIAGIONI, L. CADEDDU and T. GRAMCHEV, Semilinear parabolic equations with singular initial data in anisotropic weighted spaces. To appear in Diff. and Integral Equations.
3. 3. Comm. P.D.E., 21, 1996, pp. 179-193.
4. s. N.A.T.M.A. 14, 1990, pp. 807-836.
5. [CW2] T. CAZENAVE and F. WEISSLER, Asymptotically self-similar global solutions of the non linear Schrödinger and heat equations. Math. Z. (to appear).
6. [CW3] T. CAZENAVE and F. WEISSLER, More self-similar solutions of the nonlinear Schrödinger equation. No. D.E.A. (to appear).
7. s solutions and unconditional well-posedness. J. Ana. Math. 67, 1995, pp. 281-306.
8. [KW] O. KAVIAN and WEISSLER F., Self-similar solutions of the pseudo-conformally invariant Schrödinger equation, Michigan Math. J. 41, 1994, pp. 151-173.
9. [Ma] J. MARSCHALL, Nonregular pseudo-differential operators. Z. Anal. Anwendungen 15, 1996, pp. 109-148.
10. [R] F. RIBAUD, Thèse Université Paris XI, 1996.
11. [RY] F. RIBAUD and A. Youssfi Self-similar solutions of the nonlinear wave equations. (to appear).
12. [RS] T. RUNST and W. SICKEL, Sobolev spaces of fractional order, Nemytskii operators and nonlinear partial differential equations. de Gruyter, Berlin, 1996.
13. [RX] J. RUSSELL and P. XINBING, On a elliptic equation related to the blow up phenomena in the nonlinear Schrödinger equation. Pr. Royal Soc. Edinburgh 123 A, 1993, pp. 763-782.
14. [St] S. STEIN, Singular integral and differential properties of functions. Princeton Univ. Press, Princeton (1970).
15. [SY] W. SICKEL and A. YOUSSFI, The characterization of the regularity of the Jacobian determinant in the framework of potential spaces. J. London Math. Soc. (to appear).