Semi-classical states of nonlinear Schrödinger equations: A variational reduction method

Mathematische Annalen

Volumn 324, Issue 1, 2002, Pages 1-32

  Del Pino, Manuel ^a   Felmer, Patricio ^a  

^a UNIVERSITY OF CHILE   (Chile)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036026058     PISSN: 00255831     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002080200327     Document Type: Article

References (32)

1. A. Ambrosetti, M. Badiale, S. Cingolani, Semiclassical states of nonlinear Schrödinger equations. Arch. Rat. Mech. Anal. 140, (1997), 285-300
2. V. Benci, D. Fortunato, L. Pisani, Soliton like solutions of a Lorenz invariant equation in dimension 3. Reviews in Mathematical Physics, 3 (1998), 315-344
3. H. Berestycki, P.L. Lions, Nonlinear Scalar Field Equations I, Existence of a ground state. Arch. Rat. Mech. Anal. 82 (1983) 313-345
4. F. Bethuel, H. Brezis, F. Hélein, Ginzburg-Landau Vortices. PNLDE, 13, Birkhäuser, 1994. Boston
5. C.-C. Chen, C.-S.Lin, Uniqueness of the ground state solution of Δu + f(u) = 0. Comm. in P.D.E. 16 (1991), 1549-1572
6. N. Comm. Pure and Applied Math, Vol. XLV (1992), 1217-1269
7. V. Coti Zelati, P. Rabinowitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials. J. Amer. Math. Soc. 4 (1992), 693-727
8. M. del Pino, P. Felmer, Local mountain passes for semilinear elliptic problems in unbounded domains. Calc. Var. 4 (1996), 121-137
9. M. del Pino, P. Felmer, Multi-peak bound states of nonlinear Schrödinger equations. AIHP, Analyse Nonlineaire, Vol. 15, No2 (1998), 127-149
10. M. del Pino, P. Felmer, Semi classical states for Nonlinear Schrö- dinger equations Journal of Functional Analysis Vol. 149, No 1 (1997), 245-265
11. M. del Pino, P. Felmer, Spike-layered solutions of singularly perturbed elliptic problems in a degenerate setting. Indiana University Mathematical Journal Vol. 48, No 3 (1999), 883-898
12. M. del Pino, C. Flores, Asymptotic behavior of best constants and extremals of subcritical trace embeddings in expanding domains. Comm. in PDE 26 (2001), 2189-2210
13. A. Floer, A. Weinstein, Nonspreading Wave Packets for the Cubic Schrödinger Equation with a Bounded Potential. Journal of Functional analysis 69 (1986), 397-408
14. N. Advances in Math. Studies 7 A (1979), 209-243
15. M. Grossi, Some results on a class of nonlinear Schrödinger equations. To appear Math. Z.
16. n. Arch. Rat. Mech. Anal. 105 (1989), 243-266
17. X. Kang, J. Wei, On interacting bumps of semiclassical states of nonlinear Schröduinger equations. Adv. Diff. Eqns 5 (2000), 899-928 4 1991, 583-599
18. X. Kang, J. Wei, On interacting bumps of semiclassical states of nonlinear Schröduinger equations. Adv. Diff. Eqns 5 (2000), 899-928 4 1991, 583-599
19. Y. Y. Li, On a singularly perturbed elliptic equation. Advances in Differential Equations 2 (1997), 955-980
20. P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case. Part II. Analyse Nonlin. 1 (1984), 223-283
21. W.M. Ni, I. Takagi, On the shape on least-energy solutions to a semilinear Neumann problem. Comm. on Pure and App. Math. Vol. XLIV (1991), 819-851
22. W.-M. Ni, I. Takagi, Locating the peaks of least-energy solutions to a semilinear Neumann problem. Duke Math. J. 70 (1993), 247-281
23. W.-M. Ni, J. Wei, On the location and profile of spike-layer solutions to singularly perturbed semilinear Dirichlet problems. Comm. Pure Appl. Math. 48 (1995), 731-768
24. a. Comm. Partial Diff. Eq. 13 (1988), 1499-1519
25. Y.J. Oh, On positive multi-lump bound states nonlinear Schrödinger equations under multiple well potential. Comm. Math. Phys. 131 (1990), 223-253
26. A. Pistoia, Multi-peak solutions for a class of nonlinear Schrödinger equations, preprint
27. P. Rabinowitz, On a class of nonlinear Schrödinger equations. Z. Angew Math Phys 43 (1992), 270-291
28. O. Rey, The role of Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent. J. Funct. Anal. 89 (1990), 1-52
29. J. Serrin, M. Tang, Uniqueness of ground states for quasilinear elliptic equations. Indiana Univ. Math. J. 49 (2000), 897-923
30. G. Spradlin, Ph.D. Thesis University of Wisconsin, 1994
31. N. Thandi, Ph.D. Thesis University of Wisconsin, 1995
32. X. Wang, On concentration of positive bound states of nonlinear Schrödinger equations. Comm. Math. Phys. 153(2) (1993), 229-244