Asymptotic Properties of Solutions to Semilinear Equations Involving Multiple Critical Exponents
Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 537-547

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

In this paper, we investigate a semilinear elliptic equation that involves multiple Hardy-type terms and critical Hardy–Sobolev exponents. By the Moser iteration method and analytic techniques, the asymptotic properties of its nontrivial solutions at the singular points are investigated.
DOI : 10.4153/CMB-2011-101-4
Mots-clés : 35B33, 35B40, 35J60, elliptic problem, solution, Hardy–Sobolev inequality, singularity, Moser iteration
Kang, Dongsheng. Asymptotic Properties of Solutions to Semilinear Equations Involving Multiple Critical Exponents. Canadian mathematical bulletin, Tome 55 (2012) no. 3, pp. 537-547. doi: 10.4153/CMB-2011-101-4
@article{10_4153_CMB_2011_101_4,
     author = {Kang, Dongsheng},
     title = {Asymptotic {Properties} of {Solutions} to {Semilinear} {Equations} {Involving} {Multiple} {Critical} {Exponents}},
     journal = {Canadian mathematical bulletin},
     pages = {537--547},
     year = {2012},
     volume = {55},
     number = {3},
     doi = {10.4153/CMB-2011-101-4},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-101-4/}
}
TY  - JOUR
AU  - Kang, Dongsheng
TI  - Asymptotic Properties of Solutions to Semilinear Equations Involving Multiple Critical Exponents
JO  - Canadian mathematical bulletin
PY  - 2012
SP  - 537
EP  - 547
VL  - 55
IS  - 3
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-101-4/
DO  - 10.4153/CMB-2011-101-4
ID  - 10_4153_CMB_2011_101_4
ER  - 
%0 Journal Article
%A Kang, Dongsheng
%T Asymptotic Properties of Solutions to Semilinear Equations Involving Multiple Critical Exponents
%J Canadian mathematical bulletin
%D 2012
%P 537-547
%V 55
%N 3
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-2011-101-4/
%R 10.4153/CMB-2011-101-4
%F 10_4153_CMB_2011_101_4

[1] [1] Abdellaoui, B., Felli, V., and Peral, I., Existence and multiplicity for perturbations of an equation involving Hardy inequality and critical Sobolev exponent in the whole N. Adv. Differential Equations 9(2004), no. 5-6, 481–508. Google Scholar

[2] [2] Ambrosetti, A. and Rabinowitz, P. H., Dual variational methods in critical point theory and applications. J. Functional Analysis 14(1973), 349–381. Google Scholar | DOI

[3] [3] Brézis, H. and Nirenberg, L., Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36(1983) no. 4, 437–477. Google Scholar | DOI

[4] [4] Caffarelli, L., Kohn, R., and Nirenberg, L., First order interpolation inequality with weights. Compositio Math. 53(1984), no. 3, 259–275. Google Scholar

[5] [5] Cao, D. and Han, P., Solutions to critical elliptic equations with multi-singular inverse square potentials. J. Differential Equations 224(2006), no. 2, 332–372. Google Scholar | DOI

[6] [6] Catrina, F. and Wang, Z.-Q., On the Caffarelli-Kohn-Nirenberg inequalities: sharp constants, existence (and nonexistence), and symmetry of extermal functions. Comm. Pure Appl. Math. 54(2001), no. 2, 229–258. Google Scholar | DOI

[7] [7] Chou, K. and Chu, C., On the best constant for a weighted Sobolev-Hardy inequality. J. London Math. Soc. 48(1993), no. 1, 137–151. Google Scholar | DOI

[8] [8] Dautray, R. and Lions, P., Mathematical Analysis and Numerical Methods for Science and Technology. I. Physical Origins and Classical Methods. Springer-Verlag, Berlin, 1990. Google Scholar

[9] [9] Felli, V. and Terracini, S., Elliptic equations with multi-singular inverse-square potentials and critical nonlinearity. Comm. Partial Differential Equations 31(2006), no. 1-3, 469–495. Google Scholar | DOI

[10] [10] Ghoussoub, N. and Yuan, C., Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents,. Trans. Amer. Math. Soc. 352(2000), no. 12, 5703–5743. Google Scholar | DOI

[11] [11] Hardy, G., Littlewood, J., and Pólya, G., Inequalities. Cambridge University Press, Cambridge, UK, 1934. Google Scholar

[12] [12] Huang, Y. and Kang, D., Elliptic systems involving the critical exponents and potentials. Nonlinear Anal. 71(2009), no. 9, 3638–3653. Google Scholar | DOI

[13] [13] Jannelli, E., The role played by space dimension in elliptic critical problems. J. Differential Equations 156(1999), no. 2, 407–426. Google Scholar | DOI

[14] [14] Kang, D. and Li, G., On the elliptic problems involving multi-singular inverse square potentials and multi-critical Sobolev-Hardy exponents. Nonlinear Anal. 66(2007) , no. 8, 1806–1816. Google Scholar | DOI

[15] [15] Kang, D. and Peng, S., Positive solutions for singular critical elliptic problems. Appl. Math. Lett. 17(2004), no. 4, 411–416. Google Scholar | DOI

[16] [16] Lai, B. and Zhou, S., Asymptotic behavior of positive solutions of semilinear elliptic equations in RN. II. Acta Math. Sin. (Engl. Ser.) 26(2010), no. 9, 1723–1738. Google Scholar | DOI

[17] [17] Lions, P. L., The concentration compactness principle in the calculus of variations.T the limit case. I. Rev. Mat. Iberoamericana 1(1985). no. 1, 145–201. Google Scholar

[18] [18] Lions, P. L., The concentration compactness principle in the calculus of variations. The limit case. II. Rev. Mat. Iberoamericana 1(1985), no. 2, 45–121. Google Scholar

[19] [19] Smets, D., Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities. Trans. Amer. Math. Soc. 357(2005), no. 7, 2909–2938. Google Scholar | DOI

[20] [20] Terracini, S., On positive entire solutions to a class of equations with a singular coefficient and critical exponent. Adv. Differential Equations 1(1996), no. 2, 241–264. Google Scholar

Cité par Sources :