Transactions of the American Mathematical Society

Author(s): Zhiren Jin
Journal: Trans. Amer. Math. Soc. 349 (1997), 1945-1959.
MSC (1991): Primary 35J65,, 35J25
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Abstract: Both existence and non-existence results for principal eigenvalues of an elliptic operator with indefinite weight function have been proved. The existence of a continuous family of principal eigenvalues is demonstrated.

1.: Allegretto, W., Principal eigenvalues for indefinite weight elliptic problems in $R^{n}$ , Proc. Amer. Math. Soc. 116 (1992), 701-706. MR 93a:35114
2.: Aubin, T., Nonlinear analysis on manifolds, Springer-Verlag, New York (1982). MR 85j:58002
3.: Brown, K.J., Cosner, C. & Fleckinger, J., Principal eigenvalues for problems with indefinite weight function on $R^{n}$ , Proc. Amer. Math. Soc. 109 (1990), 147-155. MR 90m:35140
4.: Brown, K.J., Lin, S.S., & Tertikas, A., Existence and nonexistence of steady-state solutions for a selection-migration model in population genetics, J. Math. Biol. 27 (1989), 91-104. MR 90i:92012
5.: Brown, K.J. & Tertikas, A., On the bifurcation of radially symmetric steady-state solutions arising in population genetics, SIAM J. Math. Anal. 22 (1991), 400-413. MR 92e:92018
6.: Brown, K.J. & Tertikas, A, The existence of principal eigenvalues for problems with indefinite weight function on $R^{k}$ , Proc. Royal Soc. Edinburgh 123A (1993), 561-569. MR 94i:35136
7.: Fleming, K.J., A selection-migration model in population genetics, J. Math. Biol. 2 (1975), 219-233. MR 53:7531
8.: Gilbarg, D. & Trudinger, N.S., Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, Berlin. (1983). MR 86c:35035
9.: Jung, Y.T., On the elliptic equations $\tfrac {4(n-1)}{n-2} \Delta u + K(x) u^{ \tfrac {n+2}{n-2}} =0$ and the conformal deformation of Riemannian metrics, Indiana Univ. Math. J. 43 (1994), 737-746. MR 96a:53052

Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 35J65,, 35J25

Zhiren Jin
Affiliation: Department of Mathematics and Statistics, Wichita State University, Wichita, Kansas 67260
Email: zhiren@cs.twsu.edu

DOI: 10.1090/S0002-9947-97-01797-2
PII: S 0002-9947(97)01797-2
Keywords: Principal eigenvalue, Laplace operator, indefinite weight function, conformal deformation on the unit sphere, maximum principles
Received by editor(s): April 3, 1995
Received by editor(s) in revised form: November 20, 1995
Copyright of article: Copyright 1997, American Mathematical Society

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