Semiclassical limit for a quasilinear elliptic field equation: One-peak and multipeak solutions

Advances in Differential Equations

Volumn 6, Issue 4, 2001, Pages 385-418

  Badiale, Marino ^a   Benci, Vieri ^b   D'Aprile, Teresa ^a  

^a SCUOLA NORMALE SUPERIORE   (Italy)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001607750     PISSN: 10799389     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. A. Ambrosetti, M. Badiale, and S. Cingolani, Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal., 140 (1997), 285-300.
2. M. Badiale, V. Benci, and T. D'Aprile, Existence, multiplicity and concentration of bound states for a quasilinear elliptic field equation, Calc. Var. PDE, to appear.
3. V. Benci, Quantum phenomena in a classical model, Foundations of Physics, 29 (1999), 1-29.
4. V. Benci and A. Abbondandolo, Solitons and Bohmian mechanics, Proc. Nat. Acad. Sciences, to appear.
5. V. Benci, P. D'Avenia, D. Fortunato, and L. Pisani, Solitons in several space dimensions: a Derrick's problem and infinitely many solutions, Arch. Rat. Mech. Anal., to appear.
6. V. Benci, D. Fortunato, and L. Pisani, Remarks on topological solitons, Topological Methods in Nonlinear Analysis, 7 (1996), 349-367.
7. V. Benci, D. Fortunato, A. Masiello, and L. Pisani, Solitons and electromagnetic field, Math. Z., 232 (1999), 349-367.
8. V. Benci and D. Fortunato, Solitons and particles, Proc. "Int. Conf. on Nonlinear Diff. Equat. and Appl.," Tata Inst. Fund. Res., Bangalore, to appear.
9. V. Benci, D. Fortunato, and L. Pisani, Soliton-like solutions of a Lorentz invariant equation in dimension 3, Reviews in Mathematical Physics, 10 (1998), 315-344.
10. V. Benci and D. Fortunato, Solitons and relativistic dynamics, Calculus of Variations and Partial Differential equations, G. Buttazzo, A. Marino and M.K.V. Murthy, editors, Springer (1999), 285-326.
11. M. Del Pino and P. Felmer, Local mountain passes for semilinear elliptic problems in unbounded domains, Calc. Var. PDE, 4 (1996), 121-137.
12. M. Del Pino and P. Felmer, Semi-classical states for nonlinear Schrödinger equations, J. Funct. Anal., 149 (1997), 245-265.
13. M. Del Pino and P. Felmer, Multi-peak bound states for nonlinear Schrödinger equations, Ann. Inst. Henri Poincarè, 15 (1998), 127-149.
14. A. Floer and A. Weinstein, Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential, J. Funct. Anal., 69 (1986), 397-408.
15. M. Grossi, Some results on a class of nonlinear Schrödinger equations, Math. Z., to appear.
16. Y.Y. Li, On a singularly perturbed elliptic equation Adv. Diff. Eqns, Vol. 2 (1997), 955-980.
17. P.L. Lions, The concentration-compactness principle in the calculus of variations. The limit case. Part I and II, Rev. Mat. Iber., 1.1 (1985), 145-200 and Vol. 1.2 (1985), 45-121.
18. a, Comm. Partial Diff. Eq., 13 (1998), 1499-1519.
19. Y.J. Oh, On positive multi-lump bound states of nonlinear Schrödinger equation under multiple well potential, Comm. Math. Phys., 131 (1990), 223-253.
20. P. Rabinowitz, On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys., Vol 43 (1992), 270-291.
21. X. Wang, On concentration of positive bound states of nonlinear Schrödinger equations, Comm. Math. Phys., 153 (1993), 229-244.