Positive solutions of nonlinear Schrödinger-Poisson systems with radial potentials vanishing at infinity

Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni

Volumn 19, Issue 3, 2008, Pages 211-227

  Mercuri, Carlo ^a  

^a SISSA   (Italy)

Author keywords

Nonlinear Schrodinger equations; Palais Smale condition; Pohozaev identity; Weighted Sobolev spaces

Indexed keywords

EID: 84887254058     PISSN: 11206330     EISSN: 17200768     Source Type: Journal    
DOI: 10.4171/RLM/520     Document Type: Article

References (15)

1. A. AMBROSETTI - V. FELLI - A. MALCHIODI, Ground states of nonlinear Schrödinger equations with potentials vanishing at infinity. J. Eur. Math. Soc. 7 (2005), 117-144. (Pubitemid 40167001)
2. A. AMBROSETTI - A. MALCHIODI, Nonlinear Analysis and Semilinear Elliptic Problems. Cambridge Stud. Adv. Math. 104, Cambridge Univ. Press, 2007.
3. A. AMBROSETTI - P. H. RABINOWITZ, Dual variational methods in critical point theory and applications. J. Funct. Anal. 14 (1973), 349-381.
4. A. AMBROSETTI - D. RUIZ, Multiple bound states for the Schrödinger-Poisson problem. Comm. Contemp. Math. 10 (2008), 1-14.
5. H. BERESTYCKI - P. L. LIONS, Nonlinear scalar field equations, I: Existence of a ground state. Arch. Ration. Mech. Anal. 82 (1983), 313-345. (Pubitemid 13555203)
6. D. CASSANI, Existence and non-existence of solitary waves for critical Klein-Gordon equation coupled with Maxwell equations. Nonlinear Anal. 58 (2004), 733-747.
7. T. D'APRILE - D. MUGNAI, Non-existence results for the coupled Klein-Gordon-Maxwell and Schrödinger-Maxwell equations. Adv. Nonlinear Stud. 4 (2004), 307-322. (Pubitemid 39289313)
8. N. Indiana Univ. Math. J. 54 (2005), 443-464. (Pubitemid 40778019)
9. O. KAVIAN, Introduction à la théorie des points critiques et applications aux problèmes elliptiques. Springer, Paris, 1993.
10. P.-L. LIONS, Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys. 109 (1984), 33-97.
11. B. OPIC - A. KUFNER, Hardy-Type Inequalities. Pitman Res. Notes in Math. Ser. 219, Longman Sci. Tech., Harlow, 1990.
12. D. RUIZ, The nonlinear Schrödinger-Poisson equation under the effect of a nonlinear local term. J. Funct. Anal. 237 (2006), 655-674. (Pubitemid 43792923)
13. W. A. STRAUSS, Existence of solitary waves in higher dimensions. Comm. Math. Phys. 55 (1977), 149-162.
14. J. SU - Z. Q. WANG - M. WILLEM, Weighted Sobolev embedding with unbounded and decaying radial potentials. J. Differential Equations 238 (2007), 201-219.
15. M. STRUWE, Variational Methods: Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems. 3rd ed., Springer, Berlin, 2000.