Normalized solutions of nonlinear Schrödinger equations

Archiv der Mathematik

Volumn 100, Issue 1, 2013, Pages 75-83

  Bartsch, Thomas ^a   de Valeriola, Sébastien ^b  

^a JUSTUS LIEBIG UNIVERSITY   (Germany)

^b Institut de Mathématique   (Belgium)

Author keywords

Nonlinear eigenvalue problem; Nonlinear Schr dinger equation; Normalized solutions; Radial solutions

Indexed keywords

EID: 84872683309     PISSN: 0003889X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00013-012-0468-x     Document Type: Article

References (12)

1. T. Bartsch, Topological methods for variational problems with symmetries, Lecture Notes in Mathematics 1560, Springer-Verlag, Berlin 1993.
2. Bartsch T.: Infinitely many solutions of a symmetric Dirichlet Problem. Nonlin. Anal. 20, 1205-1216 (1993).
3. Berestycki H, Lions P.-L: Nonlinear scalar field equations I. Arch. Rat. Mech. Anal. 82, 313-345 (1983).
4. Berestycki H, Lions P.-L: Nonlinear scalar field equations, II. Arch. Rat. Mech. Anal. 82, 347-375 (1983).
5. P. E. Conner and E. E. Floyd, Fixed point free involutions and equivariant maps. II., Trans. Amer. Math. Soc. 105, 222-228.
6. Fadell E. R, Rabinowitz P. H: Bifurcation for odd potential operators and an alternative topological index. J. Funct. Anal. 26, 48-67 (1977).
7. Hajaiej H, Stuart C: Existence and non-existence of Schwarz symmetric ground states for elliptic eigenvalue problems, Ann. Mat. Pura Appl. 184, 297-314 (2005).
8. N: mountain pass and symmetric mountain pass approaches, Top. Meth. Nonlin. Anal. 35, 253-276 (2010).
9. Jeanjean L.: Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlin. Anal. 28, 1633-1659 (1997).
10. P. G. Kevrekidis, d. J. Frantzeskakis, and R. Carretero-Gonzalez (eds.), Emergent Nonlinear Phenomena in Bose-Einstein Condensation, Springer-Verlag, Berlin 2008.
11. P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Reg. Conf. Ser. Math. 65, Amer. Math. Soc., Providence 1986.
12. M. Willem, Minimax Methods, Birkhäuser, Boston 1996.