Nonradial solutions of semilinear elliptic equations on annuli

Norimichi HIRANO; Noriko MIZOGUCHI

doi:10.2969/jmsj/04610111

Norimichi HIRANO, Noriko MIZOGUCHI

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ジャーナルフリー

1994 年 46 巻 1 号 p. 111-117

DOI https://doi.org/10.2969/jmsj/04610111

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Published: 1994 Received: 1992/09/18 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.
2) H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
3) C. V. Coffman, A nonlinear boundary value problem with many positive solutions, J. Differential Equation, 54 (1984), 429-437.
4) B. Gidas, W. M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
5) N. Hirano, Existence of solutions for semilinear elliptic equations on a strip-like domain, preprint.
6) H. Hofer, A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem, J. London Math. Soc., 31 (1985), 566-570.
7) B. Kawohl, Rearrangements and convexity of level sets in P. D. E., Lecture Notes in Math., 1150, Springer, 1985.
8) A. C. Lazer and S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Anal., 12 (1988), 761-775.
9) Y. Y. Li, Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equation, 83 (1990), 348-367.
10) S. S. Lin, Existence of many positive nonradial solutions for nonlinear elliptic equations on annulus, preprint.
11) T. Suzuki, Radial and nonradial solutions for semilinear elliptic equations on circular domains, In INdAM Conference on geometry of solutions of partial differential equations, Cortona 1988, (ed. G. Talenti), Simposia Mathematica, 30, Academic Press, 1989, pp. 153-174.
12) T. Suzuki, Generation of positive nonradial solutions for semilinear elliptic equations on annuli: a variational approach, preprint.

Right : [1] A. Ambrosetti and P. H. Rabinowitz, Dual variational methods in critical point theory and applications, J. Funct. Anal., 14 (1973), 349-381.
[2] H. Brezis and L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents, Comm. Pure Appl. Math., 36 (1983), 437-477.
[3] C. V. Coffman, A nonlinear boundary value problem with many positive solutions, J. Differential Equation, 54 (1984), 429-437.
[4] B. Gidas, W. M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979), 209-243.
[5] N. Hirano, Existence of solutions for semilinear elliptic equations on a strip-like domain, preprint.
[6] H. Hofer, A geometric description of the neighbourhood of a critical point given by the mountain-pass theorem, J. London Math. Soc., 31 (1985), 566-570.
[7] B. Kawohl, Rearrangements and convexity of level sets in P. D. E., Lecture Notes in Math., 1150, Springer, 1985.
[8] A. C. Lazer and S. Solimini, Nontrivial solutions of operator equations and Morse indices of critical points of min-max type, Nonlinear Anal., 12 (1988), 761-775.
[9] Y. Y. Li, Existence of many positive solutions of semilinear elliptic equations on annulus, J. Differential Equation, 83 (1990), 348-367.
[10] S. S. Lin, Existence of many positive nonradial solutions for nonlinear elliptic equations on annulus, preprint.
[11] T. Suzuki, Radial and nonradial solutions for semilinear elliptic equations on circular domains, In INdAM Conference on geometry of solutions of partial differential equations, Cortona 1988, (ed. G. Talenti), Simposia Mathematica, 30, Academic Press, 1989, pp. 153-174.
[12] T. Suzuki, Generation of positive nonradial solutions for semilinear elliptic equations on annuli: a variational approach, preprint.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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