Sturm theorems for degenerate elliptic equations
HTML articles powered by AMS MathViewer
- by Walter Allegretto PDF
- Proc. Amer. Math. Soc. 129 (2001), 3031-3035 Request permission
Abstract:
We employ a version of the Picone Identity, suitable for the $p$-Laplacean, to obtain a Sturm Comparison Theorem for generalized solutions. This answers a question posed by Dunninger in 1995.References
- W. Allegretto, A comparison theorem for nonlinear operators, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (3) 25 (1971), 41–46. MR 298181
- W. Allegretto, Sturm type theorems for solutions of elliptic nonlinear problems, Nonlinear Differential Equations and Applications (to appear).
- Walter Allegretto and Yin Xi Huang, A Picone’s identity for the $p$-Laplacian and applications, Nonlinear Anal. 32 (1998), no. 7, 819–830. MR 1618334, DOI 10.1016/S0362-546X(97)00530-0
- Walter Allegretto and Yin Xi Huang, Principal eigenvalues and Sturm comparison via Picone’s identity, J. Differential Equations 156 (1999), no. 2, 427–438. MR 1705379, DOI 10.1006/jdeq.1998.3596
- D. R. Dunninger, A Sturm comparison theorem for some degenerate quasilinear elliptic operators, Boll. Un. Mat. Ital. A (7) 9 (1995), no. 1, 117–121 (English, with Italian summary). MR 1324611
- P. Erdös, On the distribution of normal point groups, Proc. Nat. Acad. Sci. U.S.A. 26 (1940), 294–297. MR 2000, DOI 10.1073/pnas.26.4.294
- J. Jaroš and T. Kusano, A Picone type identity for second order half-linear differential equations, Acta Math. Univ. Comenian. (N.S.) 68 (1999), no. 1, 137–151. MR 1711081
- Giovanni Maria Troianiello, Elliptic differential equations and obstacle problems, The University Series in Mathematics, Plenum Press, New York, 1987. MR 1094820, DOI 10.1007/978-1-4899-3614-1
Additional Information
- Walter Allegretto
- Affiliation: Department of Mathematical Sciences, University of Alberta, Edmonton, Alberta, Canada T6G 2G1
- Email: wallegre@retl.math.ualberta.ca
- Received by editor(s): March 2, 2000
- Published electronically: March 29, 2001
- Additional Notes: Research supported in part by NSERC (Canada)
- Communicated by: David S. Tartakoff
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 3031-3035
- MSC (2000): Primary 35B05; Secondary 35D99
- DOI: https://doi.org/10.1090/S0002-9939-01-05979-2
- MathSciNet review: 1840109