Existence of many positive solutions of semilinear elliptic equations on an annulus
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- by Zhi-Qiang Wang and Michel Willem PDF
- Proc. Amer. Math. Soc. 127 (1999), 1711-1714 Request permission
Abstract:
This paper is concerned with multiplicity of positive nonradial solutions of a nonlinear eigenvalue problem on an expanding annulus domain with a fixed width in $\mathbf {R}^N$ with $N\geq 4$. For $0<\lambda <\pi ^2$, we show that the number of nonrotationally equivalent nonradial solutions tends to infinity as the inner radius of the domain tends to infinity.References
- Haïm Brézis and Louis Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math. 36 (1983), no. 4, 437–477. MR 709644, DOI 10.1002/cpa.3160360405
- Charles V. Coffman, A nonlinear boundary value problem with many positive solutions, J. Differential Equations 54 (1984), no. 3, 429–437. MR 760381, DOI 10.1016/0022-0396(84)90153-0
- Bernhard Kawohl, Rearrangements and convexity of level sets in PDE, Lecture Notes in Mathematics, vol. 1150, Springer-Verlag, Berlin, 1985. MR 810619, DOI 10.1007/BFb0075060
- Yan Yan Li, Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equations 83 (1990), no. 2, 348–367. MR 1033192, DOI 10.1016/0022-0396(90)90062-T
- Song-Sun Lin, Existence of many positive nonradial solutions for nonlinear elliptic equations on an annulus, J. Differential Equations 103 (1993), no. 2, 338–349. MR 1221909, DOI 10.1006/jdeq.1993.1053
- P.-L. Lions, Symmetries and the concentration-compactness method, Nonlinear variational problems (Isola d’Elba, 1983) Res. Notes in Math., vol. 127, Pitman, Boston, MA, 1985, pp. 47–56. MR 807536
- Takashi Suzuki, Radial and nonradial solutions for semilinear elliptic equations on circular domains, Symposia Mathematica, Vol. XXX (Cortona, 1988) Sympos. Math., XXX, Academic Press, London, 1989, pp. 153–174. MR 1062611
- Zhi-Qiang Wang, Construction of multi-peaked solutions for a nonlinear Neumann problem with critical exponent in symmetric domains, Nonlinear Anal. 27 (1996), no. 11, 1281–1306. MR 1408871, DOI 10.1016/0362-546X(95)00109-9
- Michel Willem, Minimax theorems, Progress in Nonlinear Differential Equations and their Applications, vol. 24, Birkhäuser Boston, Inc., Boston, MA, 1996. MR 1400007, DOI 10.1007/978-1-4612-4146-1
Additional Information
- Zhi-Qiang Wang
- Affiliation: Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
- MR Author ID: 239651
- Email: wang@math.usu.edu
- Michel Willem
- Affiliation: Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium
- Received by editor(s): May 15, 1997
- Received by editor(s) in revised form: September 10, 1997
- Published electronically: February 11, 1999
- Communicated by: Jeffrey B. Rauch
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 1711-1714
- MSC (1991): Primary 35J20
- DOI: https://doi.org/10.1090/S0002-9939-99-04708-5
- MathSciNet review: 1476398