Abstract
The aim of the paper is to establish two dual variational formulas for the first Dirichlet eigenvalue of the second order elliptic operators on half-line. Some explicit bounds of the eigenvalue depending only on the coefficients of the operators are presented. Moreover, the corresponding problems in the discrete case and the higher-order eigenvalues in the continuous case are also studied.
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References
Egorov, Y., Kondratiev, V., On Spectral Theory of Elliptic Operators, Berlin: Birkhäuser Verlag, 1996.
Chen, M. F., Explicit bounds of the first eigenvalue, Sci. in China, Ser. A, 2000, 43(10): 1051–1059.
Chen, M. F., Variational formulas and approximation theorems for the first eigenvalue in dimension one, Sci. in China, Ser. A, 2001, 44(4): 409–418.
Chen, M. F., Wang, F. Y., Estimation of spectral gap for elliptic operators, Trans. Amer. Math. Soc., 1997, 349(3): 1239–1267.
Opic, B., Kufner, A., Hardy-type Inequalities, New York: Longman, 1990.
Chen, M. F., Analytic proof of dual variational formula for the first eigenvalue in dimension one, Sci. in China, Ser. A, 1999, 42(8): 805–815.
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Mufa, C., Zhang, Y. & Zhao, X. Dual variational formulas for the first Dirichlet eigenvalue on half-line. Sci. China Ser. A-Math. 46, 847–861 (2003). https://doi.org/10.1360/02ys0126
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DOI: https://doi.org/10.1360/02ys0126