Multiple solutions of a semilinear elliptic equation in N

Dao-Min Cao

Annales de l'I.H.P. Analyse non linéaire (1993)

  • Volume: 10, Issue: 6, page 593-604
  • ISSN: 0294-1449

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Cao, Dao-Min. "Multiple solutions of a semilinear elliptic equation in $\mathbb {R}^N$." Annales de l'I.H.P. Analyse non linéaire 10.6 (1993): 593-604. <http://eudml.org/doc/78318>.

@article{Cao1993,
author = {Cao, Dao-Min},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {semilinear elliptic equations; multiple solutions; concentration- compactness method; dual variational principle},
language = {eng},
number = {6},
pages = {593-604},
publisher = {Gauthier-Villars},
title = {Multiple solutions of a semilinear elliptic equation in $\mathbb \{R\}^N$},
url = {http://eudml.org/doc/78318},
volume = {10},
year = {1993},
}

TY - JOUR
AU - Cao, Dao-Min
TI - Multiple solutions of a semilinear elliptic equation in $\mathbb {R}^N$
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1993
PB - Gauthier-Villars
VL - 10
IS - 6
SP - 593
EP - 604
LA - eng
KW - semilinear elliptic equations; multiple solutions; concentration- compactness method; dual variational principle
UR - http://eudml.org/doc/78318
ER -

References

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  1. [1] A. Ambrosetti and P. Rabinowitz, Dual Variational Methods in Critical Point Theory and Applications, J. Funct. Anal., Vol. 14, 1973, pp. 327-381. Zbl0273.49063
  2. [2] A. Bahri and P.L. Lions, On the Existence of a Positive Solution of Semilinear Elliptic Equations in Unbounded Domains, preprint. Zbl0883.35045
  3. [3] V. Benci and G. Cerami, Positive Solutions of Semilinear Elliptic Problems in Exterior Domains, Arch. Rat. Mech. Anal., Vol. 99, 1987. pp. 283-300. Zbl0635.35036
  4. [4] H. Berestycki and P.L. Lions, Nonlinear Scalar Field Equations, I and II, Arch. Rat. Mech. Anal., Vol. 82, 1983, pp. 313-376. Zbl0533.35029
  5. [5] W.Y. Ding and W.M. Ni, On the Existence of Positive Entire Solutions of a Semilinear Elliptic Equation, Arch. Rat. Mech. Anal., Vol. 91, 1986, pp. 288-308. Zbl0616.35029
  6. [6] I. Ekeland, Nonconvex Minimization Problems, Bull. Amer. Math. Soc., Vol. 1, 1979, pp. 443-474. Zbl0441.49011
  7. [7] B. Gidas, W.M. Ni and L. Nirenberg, Symmetry of Positive Solutions of Nonlinear Elliptic Equations in Rn, Advances in Math., Supplementary Studies, Vol. 7, 1981, pp. 369-402. Zbl0469.35052
  8. [8] Y.Y. Li, On Second Order Nonlinear Elliptic Equations, Dissertation, New York Univ., 1988. 
  9. [9] P.L. Lions, The Concentration-Compactness Principle in the Calculus of Variations. The Locally Compact Case, I and II, Vol. 1, 1984, pp. 109-145 and 223-283. Zbl0541.49009
  10. [10] P.L. Lions, On Positive Solution of Semilinear Elliptic Equation in Unbounded Domains, In Nonlinear Diffusion Equations and Their Equilibrium States, Springer, New York, 1988. Zbl0685.35039
  11. [11] M.K. Kwong, Uniqueness of Positive Solution of Δu-u+up=0, Arch. Rat. Mech. Anal., Vol. 105, 1977, pp. 169- 
  12. [12] W. Strauss, Existence of Solitary Waves in Higher Dimensions, Comm. Math. Phys., Vol. 55, 1977, pp. 109-162. [13] X.P. Zhu, Multiplie Entire Solutions of Semilinear Elliptic Equations, Nonlinear Anal., Vol. 12, 1988, pp. 1297-1316. Zbl0356.35028

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