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 2024 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.

 

Nonradial solutions of a Neumann Hénon equation on a ball
HTML articles powered by AMS MathViewer

by Craig Cowan;
Proc. Amer. Math. Soc. 152 (2024), 3955-3969
DOI: https://doi.org/10.1090/proc/16897
Published electronically: July 29, 2024

Abstract:

In this work we examine the existence of positive classical solutions of \begin{equation*} \begin {cases} -\Delta u +u = |x|^\alpha u^{p-1} & \text { in } B_1, \\ u>0 & \text { in } B_1, \\ \partial _\nu u= 0 & \text { on } \partial B_1, \end{cases} \end{equation*} where $p>1$, $\alpha >0$ and $B_1$ is the unit ball in ${\mathbb {R}}^N$ where $N \ge 4$ and is even. Of particular interest is the existence of nonradial position classical solutions. We show that under suitable conditions on $p,\alpha$ and $N$ there are positive classical nonradial solutions. Our approach is to utilize a variational approach on suitable convex cones.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2020): 35J15, 35J20, 35J60
  • Retrieve articles in all journals with MSC (2020): 35J15, 35J20, 35J60
Bibliographic Information
  • Craig Cowan
  • Affiliation: Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada
  • MR Author ID: 815665
  • Email: craig.cowan@umanitoba.ca
  • Received by editor(s): August 16, 2023
  • Received by editor(s) in revised form: March 31, 2024
  • Published electronically: July 29, 2024
  • Communicated by: Ryan Hynd
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 152 (2024), 3955-3969
  • MSC (2020): Primary 35J15, 35J20, 35J60
  • DOI: https://doi.org/10.1090/proc/16897
  • MathSciNet review: 4781987