Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

The interval of resolvent-positivity for the biharmonic operator
HTML articles powered by AMS MathViewer

by Michael Ulm PDF
Proc. Amer. Math. Soc. 127 (1999), 481-489 Request permission

Abstract:

For an operator $A$ on a Banach lattice we examine the interval on the real line for which the resolvent $\left ( \lambda - A \right )^{-1}$ is positive. This positivity interval is then explicitly calculated for the biharmonic operator $A f = - f''''$ with three different boundary conditions.
References
  • Wolfgang Arendt, Charles J. K. Batty, and Derek W. Robinson, Positive semigroups generated by elliptic operators on Lie groups, J. Operator Theory 23 (1990), no. 2, 369–407. MR 1066813
  • Charles V. Coffman, On the structure of solutions $\Delta ^{2}u=\lambda u$ which satisfy the clamped plate conditions on a right angle, SIAM J. Math. Anal. 13 (1982), no. 5, 746–757. MR 668318, DOI 10.1137/0513051
  • Robert Dautray and Jacques-Louis Lions, Mathematical analysis and numerical methods for science and technology. Vol. 2, Springer-Verlag, Berlin, 1988. Functional and variational methods; With the collaboration of Michel Artola, Marc Authier, Philippe Bénilan, Michel Cessenat, Jean Michel Combes, Hélène Lanchon, Bertrand Mercier, Claude Wild and Claude Zuily; Translated from the French by Ian N. Sneddon. MR 969367, DOI 10.1007/978-3-642-61566-5
  • Günther Greiner, Jürgen Voigt, and Manfred Wolff, On the spectral bound of the generator of semigroups of positive operators, J. Operator Theory 5 (1981), no. 2, 245–256. MR 617977
  • H.-C. Grunau and G. Sweers, Positivity for equations involving polyharmonic operators with Dirichlet boundary conditions, TWI report 95-56, TU Delft, 1995; Math. Ann. 307 (1997), 589–626.
  • V. A. Kozlov, V. A. Kondrat′ev, and V. G. Maz′ya, On sign variability and the absence of “strong” zeros of solutions of elliptic equations, Izv. Akad. Nauk SSSR Ser. Mat. 53 (1989), no. 2, 328–344 (Russian); English transl., Math. USSR-Izv. 34 (1990), no. 2, 337–353. MR 998299, DOI 10.1070/IM1990v034n02ABEH000649
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 34L40, 35B50, 47A10
  • Retrieve articles in all journals with MSC (1991): 34L40, 35B50, 47A10
Additional Information
  • Michael Ulm
  • Affiliation: Abteilung Mathematik V, Universität Ulm, D-89069 Ulm, Germany
  • Email: ulm@mathematik.uni-ulm.de
  • Received by editor(s): April 19, 1996
  • Received by editor(s) in revised form: May 22, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 481-489
  • MSC (1991): Primary 34L40, 35B50, 47A10
  • DOI: https://doi.org/10.1090/S0002-9939-99-04556-6
  • MathSciNet review: 1468205