Existence of multi-bump solutions for nonlinear Schrödinger equations via variational method

Communications in Partial Differential Equations

Volumn 21, Issue 5-6, 1996, Pages 787-820

  Gui, Changfeng ^a,b  

^a MCMASTER UNIVERSITY   (Canada)

^b UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000616123     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309608821208     Document Type: Article

References (27)

1. S. Alama and Y.Y. Li, On "multibump" bound states for certain semilinear elliptic equations, Indiana Univ. Math. J. 41 (1992), 983-1025.
2. H. Brezis and T. Kato, Remarks on the Schrödinger operators with singular complex potential, J. Math. Pure et Appl. 58 (1979), 137-151.
3. H. Berestycki and P.L. Lions, Nonlinear scalar field equations I, Existence, of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313-375.
4. V. Coti Zelati, I. Ekeland and E. Séré, A variational approach to homoclinic orbits m Hamiltonian systems, Math. Ann. 288 (1990), 133-160.
5. n,n ≥ 3, Comm. Partial Diff. Eq. 16 (1991), 1549-1572.
6. V. Coti Zelati and P.H. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc. 4 (1991), 693-727.
7. n, Comm. Pure Appl. Math. 45 (1992), 1217-1269.
8. M. del Pino and P. Felmer, Local Mountain Passes for semilinear elliptic problems in unbounded domains, preprint.
9. A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, Journal of Functional Analysis 69 (1986), 397-408.
10. C. Gui, A remark on nonlinear Schrödinger equations, Unpublished Note, (1992).
11. C. Gui, Multi-peak solutions for a semilinear Neumann problem, preprint.
12. D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, 2nd edition, Grundlehren Math. Wiss. 224, Springer-Verlag, Berlin, (1983).
13. M.K. Kwong and L. Zhang, Uniqueness of the positive solutions of Au + f(u) = 0 in an annulus, Differential Integral Equations 4 (1991), 583-599.
14. 3, Comm. Pure Appl. Math. 46 (1993), 303-340.
15. 4 and related problems, J. Functional Analysis 118 (1993), 43-118.
16. n and related problems, to appear in J. Differential Equations.
17. P.L. Lions, The concentration compactness principle in the calculus of variations. The locally compact case. Part I & II, Analyse Nonlin. 1 (1984), 109-145, 223-283.
18. W.-M. Ni and I. Takagi, On the shape of least-energy solutions to a semilinear Neumann problem, Comm. Pure Appl. Math. 44 (1991), 819-851.
19. a, Comm. Partial Diff. Eq. 13 (1988), 1499-1519.
20. a, Comm. Partial Diff. Eq. 14 (1989), 833-834.
21. Y.J. Oh, On positive multi-lump bound states of nonlinear Schrödinger equations under multiple well potential, Comm. Math. Phys. 131 (1990), 223-253.
22. P.H. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew Math. Phys. 43 (1992), 270-291.
23. P.H. Rabinowitz, Minimax Methods in Critical Points Theory with Application to Differential Equations, C.B.M.S. Reg. Conf. Ser. 65, Amer. Math. Soc., Providence, RI, (1986).
24. n, Nonlinear Analysis, a tribute in honor of Giovanni Prodi, Quaderni Scuola, Normale Superiori, Pisa, (1991), 307-318.
25. E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems. Math. Z. 209 (1992), 27-42.
26. X. Wang, On the concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys. 153 (1993), 229-244.
27. X.P. Zhu, Multiple entire solutions of a semilinear elliptic equation, Nonlinear Analysis 12 (1988), 1297-1316.