Asymptotic behavior of solutions to semilinear elliptic equations with Hardy potential

Author:
Pigong Han

Journal:
Proc. Amer. Math. Soc. **135** (2007), 365-372

MSC (2000):
Primary 35J65, 58E05

Published electronically:
August 1, 2006

MathSciNet review:
2255282

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be an open bounded domain in with smooth boundary , . We are concerned with the asymptotic behavior of solutions for the elliptic problem:

**132**(2004), 3225-3229, is wrong.

**1.**J. P. García Azorero and I. Peral Alonso,*Hardy inequalities and some critical elliptic and parabolic problems*, J. Differential Equations**144**(1998), no. 2, 441–476. MR**1616905**, 10.1006/jdeq.1997.3375**2.**Jianqing Chen,*Exact local behavior of positive solutions for a semilinear elliptic equation with Hardy term*, Proc. Amer. Math. Soc.**132**(2004), no. 11, 3225–3229. MR**2073296**, 10.1090/S0002-9939-04-07567-7**3.**Kai Seng Chou and Chiu Wing Chu,*On the best constant for a weighted Sobolev-Hardy inequality*, J. London Math. Soc. (2)**48**(1993), no. 1, 137–151. MR**1223899**, 10.1112/jlms/s2-48.1.137**4.**Daomin Cao and Pigong Han,*Solutions for semilinear elliptic equations with critical exponents and Hardy potential*, J. Differential Equations**205**(2004), no. 2, 521–537. MR**2092869**, 10.1016/j.jde.2004.03.005**5.**L. Caffarelli, R. Kohn, and L. Nirenberg,*First order interpolation inequalities with weights*, Compositio Math.**53**(1984), no. 3, 259–275. MR**768824****6.**Henrik Egnell,*Elliptic boundary value problems with singular coefficients and critical nonlinearities*, Indiana Univ. Math. J.**38**(1989), no. 2, 235–251. MR**997382**, 10.1512/iumj.1989.38.38012**7.**Ivar Ekeland and Nassif Ghoussoub,*Selected new aspects of the calculus of variations in the large*, Bull. Amer. Math. Soc. (N.S.)**39**(2002), no. 2, 207–265 (electronic). MR**1886088**, 10.1090/S0273-0979-02-00929-1**8.**Alberto Ferrero and Filippo Gazzola,*Existence of solutions for singular critical growth semilinear elliptic equations*, J. Differential Equations**177**(2001), no. 2, 494–522. MR**1876652**, 10.1006/jdeq.2000.3999**9.**David Gilbarg and Neil S. Trudinger,*Elliptic partial differential equations of second order*, 2nd ed., Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 224, Springer-Verlag, Berlin, 1983. MR**737190****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), no. 12, 5703–5743. MR**1695021**, 10.1090/S0002-9947-00-02560-5**11.**Enrico Jannelli,*The role played by space dimension in elliptic critical problems*, J. Differential Equations**156**(1999), no. 2, 407–426. MR**1705383**, 10.1006/jdeq.1998.3589**12.**D. Ruiz and M. Willem,*Elliptic problems with critical exponents and Hardy potentials*, J. Differential Equations**190**(2003), no. 2, 524–538. MR**1970040**, 10.1016/S0022-0396(02)00178-X**13.**Didier Smets,*Nonlinear Schrödinger equations with Hardy potential and critical nonlinearities*, Trans. Amer. Math. Soc.**357**(2005), no. 7, 2909–2938 (electronic). MR**2139932**, 10.1090/S0002-9947-04-03769-9

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC (2000):
35J65,
58E05

Retrieve articles in all journals with MSC (2000): 35J65, 58E05

Additional Information

**Pigong Han**

Affiliation:
Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China

Email:
pghan@amss.ac.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-06-08462-0

Received by editor(s):
April 8, 2005

Received by editor(s) in revised form:
August 11, 2005

Published electronically:
August 1, 2006

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.