On positivity, criticality, and the spectral radius of the shuttle operator for elliptic operators
Yehuda Pinchover
Source: Duke Math. J. Volume 85, Number 2
(1996), 431-445.
First Page:
Show
Hide
Full-text: Access denied (no subscription
detected)
We're sorry, but we are unable to provide
you with the full text of this article because we are not able to identify
you as a subscriber.
If you have a personal subscription to
this journal, then please login. If you are already logged in, then you
may need to update your profile to register your subscription. Read more about accessing full-text
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077243254
Mathematical Reviews number (MathSciNet): MR1417623
Zentralblatt MATH identifier: 0901.35016
Digital Object Identifier: doi:10.1215/S0012-7094-96-08518-X
References
[1] M. Brelot, On topologies and boundaries in potential theory, Enlarged edition of a course of lectures delivered in 1966. Lecture Notes in Mathematics, Vol. 175, Springer-Verlag, Berlin, 1971.
Mathematical Reviews (MathSciNet): MR43:7654
Zentralblatt MATH: 0222.31014
[2] K. L. Chung, On stopped Feynman-Kac functionals, Seminar on Probability, XIV (Paris, 1978/1979) (French), Lecture Notes in Math., vol. 784, Springer, Berlin, 1980, pp. 347–356.
Mathematical Reviews (MathSciNet): MR81m:60144
Zentralblatt MATH: 0444.60061
[3] K. L. Chung and S. R. S. Varadhan, Kac functional and Schrödinger equation, Studia Math. 68 (1980), no. 3, 249–260.
Mathematical Reviews (MathSciNet): MR82d:60145
Zentralblatt MATH: 0448.60054
[4] R. Courant and D. Hilbert, Methods of mathematical physics. Vol. II: Partial differential equations, (Vol. II by R. Courant.), Interscience Publishers (a division of John Wiley & Sons), New York-Lon don, 1962.
Mathematical Reviews (MathSciNet): MR25:4216
Zentralblatt MATH: 0099.29504
[5] F. Gesztesy and Z. Zhao, On critical and subcritical Sturm-Liouville operators, J. Funct. Anal. 98 (1991), no. 2, 311–345.
Mathematical Reviews (MathSciNet): MR93f:34146
Zentralblatt MATH: 0726.35119
Digital Object Identifier: doi:10.1016/0022-1236(91)90081-F
[6] F. Gesztesy and Z. Zhao, On positive solutions of critical Schrödinger operators in two dimensions, J. Funct. Anal. 127 (1995), no. 1, 235–256.
Mathematical Reviews (MathSciNet): MR96a:35037
Zentralblatt MATH: 0821.35035
Digital Object Identifier: doi:10.1006/jfan.1995.1010
[7] M. A. Krasnosel'skii, Positive solutions of operator equations, Translated from the Russian by Richard E. Flaherty; edited by Leo F. Boron, P. Noordhoff Ltd. Groningen, 1964.
Mathematical Reviews (MathSciNet): MR31:6107
Zentralblatt MATH: 0121.10604
[8] W. Littman, G. Stampacchia, and H. F. Weinberger, Regular points for elliptic equations with discontinuous coefficients, Ann. Scuola Norm. Sup. Pisa (3) 17 (1963), 43–77.
Mathematical Reviews (MathSciNet): MR28:4228
Zentralblatt MATH: 0116.30302
[9] M. Murata, Structure of positive solutions to $(-\Delta+V)u=0$ in $\bf R\sp n$, Duke Math. J. 53 (1986), no. 4, 869–943.
Mathematical Reviews (MathSciNet): MR88f:35039
Zentralblatt MATH: 0624.35023
Digital Object Identifier: doi:10.1215/S0012-7094-86-05347-0
Project Euclid: euclid.dmj/1077305358
[10] Y. Pinchover, On positive solutions of second-order elliptic equations, stability results, and classification, Duke Math. J. 57 (1988), no. 3, 955–980.
Mathematical Reviews (MathSciNet): MR90c:35023
Zentralblatt MATH: 0685.35035
Digital Object Identifier: doi:10.1215/S0012-7094-88-05743-2
Project Euclid: euclid.dmj/1077307221
[11] Y. Pinchover, Criticality and ground states for second-order elliptic equations, J. Differential Equations 80 (1989), no. 2, 237–250.
Mathematical Reviews (MathSciNet): MR91c:35046
Zentralblatt MATH: 0697.35036
Digital Object Identifier: doi:10.1016/0022-0396(89)90083-1
[12] Y. Pinchover, On positive Liouville theorems and asymptotic behavior of solutions of Fuchsian type elliptic operators, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), no. 3, 313–341.
Mathematical Reviews (MathSciNet): MR95h:35012
Zentralblatt MATH: 0837.35010
[13] Y. Pinchover, On the localization of binding for Schrödinger operators and its extension to elliptic operators, J. Anal. Math. 66 (1995), 57–83.
Mathematical Reviews (MathSciNet): MR96m:35061
Zentralblatt MATH: 0859.35082
Digital Object Identifier: doi:10.1007/BF02788818
[14] R. G. Pinsky, Positive harmonic functions and diffusion, Cambridge Studies in Advanced Mathematics, vol. 45, Cambridge University Press, Cambridge, 1995.
Mathematical Reviews (MathSciNet): MR96m:60179
Zentralblatt MATH: 0858.31001
[15] R. G. Pinsky, Second order elliptic operators with periodic coefficients: criticality theory, perturbations, and positive harmonic functions, J. Funct. Anal. 129 (1995), no. 1, 80–107.
Mathematical Reviews (MathSciNet): MR96b:35038
Zentralblatt MATH: 0826.35030
Digital Object Identifier: doi:10.1006/jfan.1995.1043
[16] Z. Zhao, Subcriticality, positivity and gaugeability of the Schrödinger operator, Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 513–517.
Mathematical Reviews (MathSciNet): MR91h:35104
Zentralblatt MATH: 0744.35042
Digital Object Identifier: doi:10.1090/S0273-0979-1990-15965-8
Project Euclid: euclid.bams/1183555905
[17] Z. Zhao, Subcriticality and gaugeability of the Schrödinger operator, Trans. Amer. Math. Soc. 334 (1992), no. 1, 75–96.
Mathematical Reviews (MathSciNet): MR93a:81041
Zentralblatt MATH: 0765.60063
Digital Object Identifier: doi:10.2307/2153973
JSTOR: links.jstor.org
Duke Mathematical Journal
