Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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.

 

Some counterexamples related to the stationary Kirchhoff equation
HTML articles powered by AMS MathViewer

by Jorge García-Melián and Leonelo Iturriaga PDF
Proc. Amer. Math. Soc. 144 (2016), 3405-3411 Request permission

Abstract:

In this note we consider the stationary Kirchhoff equation \[ \left \{ \begin {array}{ll} -M(\| u\|^2) \Delta u = f(x,u) & \hbox {in }\Omega ,\\ \ \ u=0 & \hbox {on }\partial \Omega , \end {array} \right . \] where $M$ is a continuous positive function and $\| \cdot \|$ is the standard norm in $H_0^1(\Omega )$. We show that the equation does not enjoy the usual comparison principles (both weak or strong) nor the sub and supersolutions method.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 35J25, 35J60
  • Retrieve articles in all journals with MSC (2010): 35J25, 35J60
Additional Information
  • Jorge García-Melián
  • Affiliation: Departamento de Análisis Matemático, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38271, La Laguna, Spain — and — Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y Fotónica, Universidad de La Laguna, C/. Astrofísico Francisco Sánchez s/n, 38203, La Laguna, Spain
  • Email: jjgarmel@ull.es
  • Leonelo Iturriaga
  • Affiliation: Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla V-110, Avda. España, 1680, Valparaíso, Chile
  • Email: leonelo.iturriaga@usm.cl
  • Received by editor(s): July 20, 2015
  • Received by editor(s) in revised form: September 25, 2015
  • Published electronically: January 26, 2016
  • Additional Notes: The first author was partially supported by Ministerio de Ciencia e Innovación and Ministerio de Economía y Competitividad under grant MTM2011-27998 (Spain) and Conicyt MEC number 80130002 (Chile)
    The second author was supported by Fondecyt number 1120524 and USM Grant 12.15.68 (Chile)
  • Communicated by: Joachim Krieger
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 3405-3411
  • MSC (2010): Primary 35J25, 35J60
  • DOI: https://doi.org/10.1090/proc/12971
  • MathSciNet review: 3503708