Existence and multiplicity of stable bound states for the nonlinear Klein-Gordon equation

Nonlinear Analysis, Theory, Methods and Applications

Volumn 72, Issue 3-4, 2010, Pages 2031-2046

  Bonanno, Claudio ^a  

^a UNIVERSITY OF PISA   (Italy)

Author keywords

Multiplicity of solutions; Nonlinear Klein Gordon equation; Solitons

Indexed keywords

BOUND STATE; GEOMETRICAL PROPERTY; MULTIPLICITY OF SOLUTIONS; NONLINEAR KLEIN-GORDON EQUATION; NONLINEAR TERMS; SOLITON-LIKE SOLUTION; SUFFICIENT CONDITIONS;

LINEAR EQUATIONS; SOLITONS;

NONLINEAR EQUATIONS;

EID: 71549141998     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2009.10.004     Document Type: Article

References (17)

1. Rosen G. Particle-like solutions to nonlinear complex scalar field theories with positive-definite energy densities. J. Math. Phys. 9 (1968) 996-998
2. Coleman S., Glaser V., and Martin A. Action minima among solutions to a class of euclidean scalar field equation. Comm. Math. Phys. 58 (1978) 211-221
3. Strauss W.A. Nonlinear Invariant Wave Equations. Lecture Notes in Physics vol. 23 (1978), Springer
4. Berestycki H., and Lions P.L. Nonlinear scalar field equations. I. Existence of a ground state. Arch. Ration. Mech. Anal. 82 (1982) 313-345
5. Shatah J. Stable standing waves of non-linear Klein-Gordon equations. Comm. Math. Phys. 91 (1983) 313-327
6. Shatah J., and Strauss W. Instability of nonlinear bound states. Comm. Math. Phys. 100 (1985) 173-190
7. Grillakis M., Shatah J., and Strauss W. Stability theory of solitary waves in the presence of symmetry, I. J. Funct. Anal. 74 (1987) 160-197
8. Statah J. Unstable ground state of nonlinear Klein-Gordon equation. Trans. Amer. Math. Soc. 290 (1985) 701-710
9. J. Bellazzini, V. Benci, C. Bonanno, A.M. Micheletti, Solitons for the nonlinear Klein-Gordon equation, Adv. Nonlinear Stud. (in press). Also at arXiv:0712.1103v1 [math.AP]
10. Benci V., and Cerami G. The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems. Arch. Ration. Mech. Anal. 114 (1991) 79-93
11. Dancer E.N. The effect of domain shape on the number of positive solutions of certain nonlinear equations. J. Differential Equations 74 (1988) 120-156
12. Benci V., Bonanno C., and Micheletti A.M. On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds. J. Funct. Anal. 252 (2007) 464-489
13. Hirano N. Multiple existence of solutions for a nonlinear elliptic problem on a Riemannian manifold. Nonlinear Anal. 70 (2008) 671-692
14. N, arXiv:0901.4459v1 [math. AP]
15. J. Bellazzini, V. Benci, C. Bonanno, E. Sinibaldi, Hylomorphic solitons in the nonlinear Klein-Gordon equations, arXiv:0810.5079v1 [math. AP]
16. Volevic L.R., and Paneyakh B.P. Certain spaces of generalized functions and embedding theorems. Russian Math. Surv. 20 (1965) 1-73
17. Palais R.S. The principle of symmetric criticality. Comm. Math. Phys. 79 (1979) 19-30