Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential
Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 19-33

Voir la notice de l'article provenant de la source Cambridge University Press

In this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of ${{\mathbb{R}}^{N}}$ . By variational methods we study the existence results.
DOI : 10.4153/CJM-2010-002-9
Mots-clés : critical Sobolev exponent, Palais–Smale condition, Linking theorem, Hardy potential
Bouchekif, Mohammed; Nasri, Yasmina. Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential. Canadian journal of mathematics, Tome 62 (2010) no. 1, pp. 19-33. doi: 10.4153/CJM-2010-002-9
@article{10_4153_CJM_2010_002_9,
     author = {Bouchekif, Mohammed and Nasri, Yasmina},
     title = {Solutions for {Semilinear} {Elliptic} {Systems} with {Critical} {Sobolev} {Exponent} and {Hardy} {Potential}},
     journal = {Canadian journal of mathematics},
     pages = {19--33},
     year = {2010},
     volume = {62},
     number = {1},
     doi = {10.4153/CJM-2010-002-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-002-9/}
}
TY  - JOUR
AU  - Bouchekif, Mohammed
AU  - Nasri, Yasmina
TI  - Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential
JO  - Canadian journal of mathematics
PY  - 2010
SP  - 19
EP  - 33
VL  - 62
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-002-9/
DO  - 10.4153/CJM-2010-002-9
ID  - 10_4153_CJM_2010_002_9
ER  - 
%0 Journal Article
%A Bouchekif, Mohammed
%A Nasri, Yasmina
%T Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential
%J Canadian journal of mathematics
%D 2010
%P 19-33
%V 62
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2010-002-9/
%R 10.4153/CJM-2010-002-9
%F 10_4153_CJM_2010_002_9

[1] [1] C. O., Alves, D. C., de Morais Filho and M. A., S. Souto, On systems of elliptic equations involving subcritical or critical Sobolev exponents. Nonlinear Anal. 42(2000), 771-787. doi:10.1016/S0362-546X(99)00121-2 Google Scholar

[2] [2] A., Ambrosetti and P. H., Rabinowitz, Dual variational methods in critical point theory and applications. J. Funct. Anal. 14(1973), 349-381. doi:10.1016/0022-1236(73)90051-7 Google Scholar

[3] [3] Brézis, H. and E., Lieb, A relation between pointwise convergence of functions and convergence of functionals. Proc. Amer.Math. Soc. 88(1983), 486-490. doi:10.2307/2044999 Google Scholar

[4] [4] Brézis, H. and L., Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36(1983), 437-477. doi:10.1002/cpa.3160360405 Google Scholar

[5] [5] A., Cappozi, D., Fortunato and G., Palmieri, An existence result for nonlinear elliptic problems involving critical Sobolev exponent. Ann. Inst. H. Poincaré Anal. Non Linéaire 2(1985), 463-470. Google Scholar

[6] [6] D., Cao and P., Han, Solutions for semilinear elliptic equations with critical exponents and Hardy potential. J. Differential Equations 205(2004), 521-537. doi:10.1016/j.jde.2004.03.005 Google Scholar

[7] [7] J., Chen, Existence of solutions for a nonlinear PDE with an inverse square potential. J. Differential Equations 195(2003), 497-519. doi:10.1016/S0022-0396(03)00093-7 Google Scholar

[8] [8] D. G., de Figueiredo, Semilinear elliptic systems. In: Lecture Notes at the Second School on Nonlinear Functional Analysis and Applications to Differential Equations at ICTP of Trieste (April 21-May 9, 1997). Google Scholar

[9] [9] A., Ferrero and F., Gazzola, Existence of solutions for singular critical growth semilinear elliptic equations. J. Differential Equations 177(2001), 494-522. doi:10.1006/jdeq.2000.3999 Google Scholar

[10] [10] N., Ghoussoub and C., Yuan, Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents. Trans. Amer.Math. Soc. 352(2000), 5703-5743. doi:10.1090/S0002-9947-00-02560-5 Google Scholar

[11] [11] E., Jannelli, The role played by space dimension in elliptic critical problems. J. Differential Equations 156(1999), 407-426. doi:10.1006/jdeq.1998.3589 Google Scholar

[12] [12] S., Terracini, On positive solutions to a class equations with singular coefficient and critical exponent. Adv. Differential Equations 1(1996), 241-264. Google Scholar

Cité par Sources :