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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
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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 $\mathbb{R}^{N}$, 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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