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Existence and uniqueness of positive eigenfunctions for certain eigenvalue systems

Published online by Cambridge University Press:  22 January 2016

Ru-Ying Xue  and
Yi-Min Yang
Ru-Ying Xue
Affiliation:
Department of Mathematics, XiXi Campus, Zhejiang University, Hangzhou 310028, Zhejiang, P. R. China, xuery@mail.hz.zj.cn
Yi-Min Yang
Affiliation:
Department of Mathematics, Hangzhou Normal College, Hangzhou 310003, Zhejiang, P. R. China
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Abstract

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The existence and uniqueness of eigenvalues and positive eigenfunctions for some quasilinear elliptic systems are considered. Some necessary and sufficient conditions which guarantee the existence and uniqueness of eigenvalues and positive eigenfunctions are given.

Keywords

35J6535D05
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 173 , 2004 , pp. 65 - 84
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2004

References

[1] Anane, A., Simpliciteét isolation de la premiére valeur propre du p-laplacien avec poids, C. R. Acad. Sci. Paris Ser. I Math., 305 (1987), no. 16, 725–728. (MR: 89e:35124).Google Scholar
[2] Otani, M. and Teshima, T., On the first eigenvalue of some quasilinear elliptic equations, Proc. Japan Acad. Ser. A Math. Sci., 64 (1988), no. 1, 8–10. (MR: 89h:35257).CrossRefGoogle Scholar
[3] Feleckinger-Pelle, J. and Takac, P., Uniqueness of positive solutions for nonlinear co-operative systems with the p-Laplacian, Indiana Univ. Math. J., 43(4) (1994), 1227–1253.CrossRefGoogle Scholar
[4] Cuesta, M. and Takac, P., A strong comparison principle for the Dirichlet p-Laplacian, Lecture Notes in Pure and Applied Mathematics, Vol. 194, 79–87.Google Scholar
[5] Lieberman, G., Boundary regularity for solutions of degenerate elliptic equations, Nonlin. Anal. T. M. A., 12(11) (1988), 1203–1219.Google Scholar
[6] Vazquez, J. L., A strong maximum principle for some quasilinear elliptic equations, Appl. Math. Optim., 12 (1984), 191–202.Google Scholar
[7] Huang, Y. X., Positive solutions of quasilinear elliptic equations, Research Reports in Math., 10 (1997), Stockholm Univ., Sweden.Google Scholar
[8] Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Rev., 18 (1978), 620–708.Google Scholar
[9] Felmer, P., Manasevich, F. R. and Thelin, F. de, Existence and uniqueness of positive solutions for certain quasilinear elliptic systems, Comm. in P. D. E., 17(11–12) (1992), 2013–2029.Google Scholar
[10] Xue, R. and Qin, Y., Existence and uniqueness of positive eigenvalues for certain eigenvalue system, System Science and Mathematical Science, 12 (1999), 175–184.Google Scholar
[11] Lindqvist, P., On the equation div(|∇u|p-2∇u) + λ|u|p-2u = 0, Proc. Amer. Math. Soc., 109 (1990), 157–164.Google Scholar
[12] Binding, P. A. and Huang, Y. X., Existence and nonexistence of positive eigenfunctions for the p-Laplacian, Proc. Amer. Math. Soc., 123(6) (1995), 1833–1838.Google Scholar