Multiplicity of positive and nodal solutions for nonlinear elliptic problems in ℝ N
Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 5, pp. 567-588. 
@article{AIHPC_1996__13_5_567_0,
     author = {Cao, Daomin and Noussair, Ezzat S.},
     title = {Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $\mathbb {R}^N$},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {567--588},
     publisher = {Gauthier-Villars},
     volume = {13},
     number = {5},
     year = {1996},
     mrnumber = {1409663},
     zbl = {0859.35032},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1996__13_5_567_0/}
}
TY  - JOUR
AU  - Cao, Daomin
AU  - Noussair, Ezzat S.
TI  - Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $\mathbb {R}^N$
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 1996
SP  - 567
EP  - 588
VL  - 13
IS  - 5
PB  - Gauthier-Villars
UR  - http://www.numdam.org/item/AIHPC_1996__13_5_567_0/
LA  - en
ID  - AIHPC_1996__13_5_567_0
ER  - 
%0 Journal Article
%A Cao, Daomin
%A Noussair, Ezzat S.
%T Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $\mathbb {R}^N$
%J Annales de l'I.H.P. Analyse non linéaire
%D 1996
%P 567-588
%V 13
%N 5
%I Gauthier-Villars
%U http://www.numdam.org/item/AIHPC_1996__13_5_567_0/
%G en
%F AIHPC_1996__13_5_567_0
Cao, Daomin; Noussair, Ezzat S. Multiplicity of positive and nodal solutions for nonlinear elliptic problems in $\mathbb {R}^N$. Annales de l'I.H.P. Analyse non linéaire, Tome 13 (1996) no. 5, pp. 567-588. http://www.numdam.org/item/AIHPC_1996__13_5_567_0/

[1] A. Bahri and J.M. Coron, On a nonlinear elliptic equation involving the Sobolev exponent: the effect of the topology of the domain, Comm. Pure Appl. Math., Vol. 41, 1988, pp. 253-294. | MR | Zbl

[2] A. Bahri and Y.Y. Li, On a min-max procedure for the existence of a positive solution for certain scalar field equation in RN ., Revista Mat. Iberoamericana, Vol. 6, 1990, pp. 1-15. | MR | Zbl

[3] A. Bahri and P.L. Lions, On the existence of a positive solution of semilinear elliptic equations in unbounded domains, preprint.

[4] V. Benci and G. Cerami, The effect of the domain topology on the number of positive solutions of nonlinear elliptic problems, Arch. Rat. Mech. Anal., Vol. 114, 1991, pp. 79-93. | MR | Zbl

[5] H. Brezis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc., Vol. 88, 1983, pp. 486-490. | MR | Zbl

[6] D.M. Cao, Positive solutions and bifurcation from the essential spectrum of a semilinear elliptic equation in RN., Nonlinear Anal. TMA., Vol. 15, 1990, pp. 1045-1052. | MR | Zbl

[7] G. Cerami and D. Passaseo, Existence and multiplicity of positive solutions for nonlinear elliptic problems in exterior domains with "rich" topology, Nonlinear Anal. TMA., Vol. 18, 1992, pp. 109-119. | MR | Zbl

[8] J.M. Coron, Topologie et cas limite des injections de Sobolev, C. R. Acad. Sc. Paris, I, Vol. 299, 1984, pp. 209-212. | MR | Zbl

[9] I. Ekeland, On the variational principle, J. Math. Anal. Appl., Vol. 17, 1974, pp. 324-353. | MR | Zbl

[10] M.K. Kwong, Uniqueness of positive solutions of Δu - u + up = 0 in RN., Arch. Rat. Mech. Anal., Vol. 105, 1989, pp. 243-266. | MR | Zbl

[11] Yi Li, Remarks on a semilinear elliptic equation on RN., J. Diff. Equats., Vol. 74, 1988, pp. 34-49. | MR | Zbl

[12] P.L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case, Ann. Inst. H. Poincaré, Analyse non linéaire, Vol. 1, 1984, pp. 102-145 and 223-283. | Numdam | MR | Zbl

[13] P.L. Lions, On positive solutions of semilinear elliptic equations in unbounded domains, in "Nonlinear Diffusion Equations and their equilibrium States", Springer, New York, 1988. | MR | Zbl

[14] M.V. Marchi and F. Pacella, On the existence of nodal solutions of the equation -Δu = |u|2*-2u with Dirichlet boundary conditions, Differential and Integral Equations, Vol. 6, 1993, pp. 849-862. | MR | Zbl

[15] D. Passaseo, Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains, Manuscripta Math., Vol. 65, 1989, pp. 147-166. | MR | Zbl

[16] G. Tarantello, On nonhomogenous elliptic equations involving critical Sobolev exponent, Ann. I.H.P. Anal. non linéaire, Vol. 9, 1992, pp. 281-304. | Numdam | MR | Zbl

[17] X.P. Zhu, Multiple entire solutions of semilinear elliptic equation, Nonlinear Anal. TMA., Vol. 12, 1988, pp. 1297-1316. | MR | Zbl