|
Infinitely many nonradial solutions to a superlinear Dirichlet problem
Author(s):
Hugo
Aduén;
Alfonso
Castro
Journal:
Proc. Amer. Math. Soc.
131
(2003),
835-843.
MSC (2000):
Primary 35J20;
Secondary 34B15
Posted:
September 17, 2002
Retrieve article in:
PDF DVI PostScript
Abstract |
References |
Similar articles |
Additional information
Abstract:
In this article we provide sufficient conditions for a superlinear Dirichlet problem to have infinitely many nonradial solutions. Our hypotheses do not require the nonlinearity to be an odd function. For the sake of simplicity in the calculations we carry out details of proofs in a ball. However, the proofs go through for any annulus.
References:
-
- 1.
- A. Bahri and P.-L. Lions, Morse index of some min-max critical points. I. Application to multiplicity results, Comm. Pure Appl. Math. 41 (1988), 1027-1037. MR 90b:58035
- 2.
- H. Berestycki and P.-L. Lions, Nonlinear scalar field equations. II. Existence of infinitely many solutions, Arch. Rat. Mech. Anal. 82 (1983), 347-375. MR 84h:35054b
- 3.
- T. Bartsch and M. Willem, Infinitely many nonradial solutions of a Euclidean scalar field equation, J. Funct. Anal. 117 (1993), 447-460. MR 94k:35093
- 4.
- A. Castro, J. Cossio, and J. M. Neuberger, On multiple solutions of a nonlinear Dirichlet problem, Nonlinear Analysis TMA 30 (1997), 3657-3662. MR 98h:35070
- 5.
- A. Castro and M. Finan, Existence of many sign-changing solutions to a superlinear Dirichlet problem on thin annuli, Topological Methods in Nonlinear Analysis. 13 (1999), 273-280. MR 2000j:35092
- 6.
- A. Castro and M. Finan, Existence of many positive nonradial solutions for a superlinear Dirichlet problem on thin annuli, Nonlinear Differential Equations, Electron. J. Diff. Eqns., Conf. 05 (2000), 21-31. MR 2001i:35116
- 7.
- A. Castro and A. Kurepa, Infinitely many radially symmetric solutions to a superlinear dirichlet problem in a ball, Proc. Amer. Math. Soc. 101 (1987), 57-64. MR 88j:35058
- 8.
- M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. Math. 106 (1977), 93-100. MR 57:13242
- 9.
- D. Fortunato and E. Jannelli, Infinitely many solutions for some nonlinear elliptic problems in symmetrical domains, Proc. Roy. Soc. Edinburgh Sect. A 105 (1987), 205-213. MR 88m:35057
- 10.
- W.-Y. Ding, On a conformally invariant equation on
 , Comm. Math. Phys. 107 (1986), 331-335. MR 87m:35066 - 11.
- M. Struwe, Superlinear elliptic boundary value problems with rotational symmetry, Arch. Math. 39 (1982), 233-240. MR 84a:35097
- 12.
- E. Yanagida, Structure of radial solutions to
 in  , SIAM J. Math. Anal. 27 (1996), 997-1014. MR 98c:35047
Similar Articles:
Retrieve articles in Proceedings of the American Mathematical Society
with MSC
(2000):
35J20,
34B15
Retrieve articles in all Journals with MSC
(2000):
35J20,
34B15
Additional Information:
Hugo
Aduén
Affiliation:
Departamento de Matemáticas, Universidad de Córdoba, Montería, Colombia
Email:
haduen@hotmail.com
Alfonso
Castro
Affiliation:
Division of Mathematics and Statistics, The University of Texas at San Antonio, San Antonio, Texas 78249
Email:
acastro@utsa.edu
DOI:
10.1090/S0002-9939-02-06642-X
PII:
S 0002-9939(02)06642-X
Keywords:
Critical point,
Morse index,
nonradial solutions,
Cwikel inequality,
nonlinear elliptic equation
Received by editor(s):
March 8, 2001
Received by editor(s) in revised form:
October 15, 2001
Posted:
September 17, 2002
Communicated by:
David S. Tartakoff
Copyright of article:
Copyright
2002,
American Mathematical Society
|
Comments: webmaster@ams.org