Duke Mathematical Journal

On positive solutions of second-order elliptic equations, stability results, and classification

Yehuda Pinchover

Article information

Source
Duke Math. J., Volume 57, Number 3 (1988), 955-980.

Dates
First available in Project Euclid: 20 February 2004

https://projecteuclid.org/euclid.dmj/1077307221

Digital Object Identifier
doi:10.1215/S0012-7094-88-05743-2

Mathematical Reviews number (MathSciNet)
MR975130

Zentralblatt MATH identifier
0685.35035

Subjects
Primary: 35B35: Stability
Secondary: 35J15: Second-order elliptic equations

Citation

Pinchover, Yehuda. On positive solutions of second-order elliptic equations, stability results, and classification. Duke Math. J. 57 (1988), no. 3, 955--980. doi:10.1215/S0012-7094-88-05743-2. https://projecteuclid.org/euclid.dmj/1077307221

References

• [1] S. Agmon, On positivity and decay of solutions of second order elliptic equations on Riemannian manifolds, Methods of Functional Analysis and Theory of Elliptic Equations (Naples, 1982) ed. D, Greco, Liguori, Naples, 1983, pp. 19–52.
• [2] S. Agmon, On positive solutions of elliptic equations with periodic coefficients in $\bf R\sp n$, spectral results and extensions to elliptic operators on Riemannian manifolds, Differential equations (Birmingham, Ala., 1983), North-Holland Math. Stud., vol. 92, North-Holland, Amsterdam, 1984, pp. 7–17.
• [3] W. Allegretto, Criticality and the $\lambda$-property for the elliptic equations, J. Differential Equations 69 (1987), no. 1, 39–45.
• [4] A. Ancona, Negatively curved manifolds, elliptic operators, and the Martin boundary, Ann. of Math. (2) 125 (1987), no. 3, 495–536.
• [5] C. Bessaga and A. Pelczyński, Selected topics in infinite-dimensional topology, PWN—Polish Scientific Publishers, Warsaw, 1975.
• [6] M. Brelot, On Topologies and Boundaries in Potential Theory, Lecture Notes in Mathematics, vol. 175, Springer-Verlag, Berlin, 1971.
• [7] R.-M. Hervé, Recherches axiomatiques sur la théorie des fonctions surharmoniques et du potentiel, Ann. Inst. Fourier (Grenoble) 12 (1962), 415–571.
• [8] 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.
• [9] Y. Pinchover, Sur les solutions positives d'équations elliptiques et paraboliques dans $\bf R^ n$, C. R. Acad. Sci. Paris Sér. I Math. 302 (1986), no. 12, 447–450.
• [10] Y. Pinchover, Positive solutions of second order elliptic equations, Ph.D. thesis, Hebrew University of Jerusalem, 1986, original in Hebrew.
• [11] Y. Pinchover, On positive solutions of elliptic equations with periodic coefficients in unbounded domains, to appear in Maximum Principles and Eigenvalue Problems in Partial Differential Equations, ed. P. W. Schaefer, Pitman Research Notes in Mathematics 175, Longman Press, London.
• [12] B. Simon, Large time behavior of the $L\spp$ norm of Schrödinger semigroups, J. Funct. Anal. 40 (1981), no. 1, 66–83.
• [13] J. C. Taylor, The Martin boundaries of equivalent sheaves, Ann. Inst. Fourier (Grenoble) 20 (1970), no. fasc. 1, 433–456.