Ground states of nonlinear Schrödinger equations with potentials

Yongqing Li; Zhi-Qiang Wang; Jing Zeng

Annales de l'I.H.P. Analyse non linéaire (2006)

  • Volume: 23, Issue: 6, page 829-837
  • ISSN: 0294-1449

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Li, Yongqing, Wang, Zhi-Qiang, and Zeng, Jing. "Ground states of nonlinear Schrödinger equations with potentials." Annales de l'I.H.P. Analyse non linéaire 23.6 (2006): 829-837. <http://eudml.org/doc/78714>.

@article{Li2006,
author = {Li, Yongqing, Wang, Zhi-Qiang, Zeng, Jing},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger equations; ground state solutions; the Ambrosetti–Rabinowitz condition},
language = {eng},
number = {6},
pages = {829-837},
publisher = {Elsevier},
title = {Ground states of nonlinear Schrödinger equations with potentials},
url = {http://eudml.org/doc/78714},
volume = {23},
year = {2006},
}

TY - JOUR
AU - Li, Yongqing
AU - Wang, Zhi-Qiang
AU - Zeng, Jing
TI - Ground states of nonlinear Schrödinger equations with potentials
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2006
PB - Elsevier
VL - 23
IS - 6
SP - 829
EP - 837
LA - eng
KW - nonlinear Schrödinger equations; ground state solutions; the Ambrosetti–Rabinowitz condition
UR - http://eudml.org/doc/78714
ER -

References

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  1. [1] A. Ambrosetti, A. Malchiodi, Perturbation Methods and Semilinear Elliptic Problems on R n , Progr. Math., Birkhäuser, in press. Zbl1115.35004MR2186962
  2. [2] Ambrosetti A., Rabinowitz P.H., Dual variational methods in critical point theory and applications, J. Funct. Anal.14 (1973) 349-381. Zbl0273.49063MR370183
  3. [3] Berestycki H., Lions P.L., Nonlinear scalar field equations. I. Existence of a ground state, Arch. Rational Mech. Anal.82 (1983) 313-345. Zbl0533.35029MR695535
  4. [4] Ding W.-Y., Ni W.-M., On the existence of positive entire solutions of a semilinear elliptic equation, Arch. Rational Mech. Anal.91 (1986) 283-308. Zbl0616.35029MR807816
  5. [5] Jeanjean L., Tanaka K., A positive solution for a nonlinear Schrödinger equation on R N , Indiana Univ. Math. J.54 (2005) 443-464. Zbl1143.35321MR2136816
  6. [6] Lions P.L., The concentration-compactness principle in the calculus of variations. The locally compact case. I & II, Ann. Inst. H. Poincaré Anal. Non Linéaire1 (1984) 109-145, 223–283. Zbl0704.49004MR778970
  7. [7] Liu J., Wang Y., Wang Z.-Q., Solutions for quasilinear Schrödinger equations via the Nehari method, Comm. Partial Differential Equations29 (2004) 879-901. Zbl1140.35399MR2059151
  8. [8] Liu Z., Wang Z.-Q., On the Ambrosetti–Rabinowitz superlinear condition, Adv. Nonlinear Stud.4 (2004) 561-572. Zbl1113.35048MR2100913
  9. [9] Rabinowitz P.H., On a class of nonlinear Schrödinger equations, Z. Angew. Math. Phys.43 (1992) 270-291. Zbl0763.35087MR1162728
  10. [10] Strauss W.A., Existence of solitary waves in higher dimensions, Comm. Math. Phys.55 (1977) 149-162. Zbl0356.35028MR454365
  11. [11] Struwe M., Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, Berlin, 2000. Zbl0746.49010MR1736116
  12. [12] Willem M., Minimax Theorems, Birkhäuser, Boston, 1996. Zbl0856.49001MR1400007

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