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Solutions to a class of Schrödinger equations
Author(s):
Yanheng
Ding
Journal:
Proc. Amer. Math. Soc.
130
(2002),
689-696.
MSC (1991):
Primary 35Q55;
Secondary 58E55
Posted:
July 25, 2001
MathSciNet review:
1866021
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Abstract:
We establish existence and multiplicity of solutions to a class of nonlinear Schrödinger equations with, e.g., ``atomic'' Hamiltonians, via critical point theory.
References:
-
- [1]
- S. Alama and Y. Y. Li, On ``Multibump'' bound states for certain semilinear elliptic equations, Indiana J. Math. 44 (1992), 983-1026. MR 94d:35044
- [2]
- S. Alama and G. Tarantello, On the solvability of a semilinear elliptic equation via an associated eigenvalue problem, Math. Z. 221 (1996), 467-493. MR 97d:35067
- [3]
- A. Ambrosetti, M. Badiale and S. Cingolani, Semiclassical states of nonlinear Schrödinger equations, Arch. Rat. Mech. Anal. 140 (1997), 285-300. MR 98k:35172
- [4]
- T. Bartsch and Y. H. Ding, On a nonlinear Schrödinger equation with periodic potential, Math. Ann. 313 (1999), 15-37. MR 99m:35218
- [5]
- R. Benguria, H. Brézis and E. H. Lieb, The Thomas-Fermi-von Weizäcker theory of atoms and molecules, Comm. Math. Phys. 79 (1981), 167-180. MR 83m:81114
- [6]
- V. Coti-Zelati and P. H. Rabinowitz, Homoclinic type solutions for a semilinear elliptic PDE on
 , Comm. Pure Appl. Math. 45 (1992), 1217-1269. MR 93k:35087 - [7]
- M. A. Del Pino and P. Felmer, Multiple solutions for a semilinear elliptic equation, Trans. Amer. Math. Soc. 347 (1995), 4839-4853. MR 96c:35062
- [8]
- W. Kryszewski and A. Szulkin, Generalized linking theorem with an application to semilinear Schrödinger equation, Adv. Diff. Eq. 3 (1998), 441-472. CMP 2000:11
- [9]
- S.J. Li and M. Willem, Applications of local linking to critical point theory, J. Math. Anal. Appl. 189 (1995), 6-32. MR 96a:58045
- [10]
- P. L. Lions, Solutions of Hartree-Fock equations for Coulomb systems, Comm. Math. Phys. 109 (1987), 33-97. MR 88e:35170
- [11]
- P.H. Rabinowitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, C. B. M. S. 65, Amer. Math. Soc., Providence, R. I., 1986. MR 87j:58024
- [12]
- P. H. Rabinowitz, On a class of nonlinear Schrödinger equations, ZAMP 43 (1992), 270-291. MR 93h:35194
- [13]
- M. Reed and B. Simon, Methods of Mathematical Physics, vol. I-IV, Academic Press, 1978. MR 58:12429a; MR 58:12429b; MR 80m:81085; MR 58:12429c
- [14]
- C. Troestler and M. Willem, Nontrivial solution of a semilinear Schrödinger equation, Comm. Partial Diff. Eq. 21 (1996), 1431-1449. MR 98i:35034
- [15]
- M. Willem, Minimax Methods, Birkhäuser, Boston, 1996.
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Additional Information:
Yanheng
Ding
Affiliation:
Morningside Center of Mathematics and Institute of Mathematics, AMSS, Chinese Academy of Sciences, 100080 Beijing, People's Republic of China
Email:
dingyh@math03.math.ac.cn
DOI:
10.1090/S0002-9939-01-06225-6
PII:
S 0002-9939(01)06225-6
Keywords:
Schr\"{o}dinger equations,
multiple solutions,
critical point theory
Received by editor(s):
August 15, 2000
Posted:
July 25, 2001
Additional Notes:
This research was supported by the Special Funds for Major State Basic Research Projects of China.
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2001,
American Mathematical Society
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