Special Issue in honor of John W. Neuberger. Electron. J. Diff. Eqns., Special Issue 02 (2023), pp. 1-10.

A nonexistence result for p-Laplacian systems in a ball

Abraham Abebe, Maya Chhetri

Abstract:
We consider the p-Laplacian system

where λ>0 is a parameter, $\Delta_p u:= \text{div}(|\nabla u|^{p-2}\nabla u)$ is the p-Laplacian operator for p>1 and Ω is a unit ball in $\mathbb{R}^N$ (N≥2). The nonlinearities $f, g: [0,\infty) \to \mathbb{R}$ are assumed to be $C^1$ strictly increasing semipositone functions (f(0)< 0 and g(0)<0) that are p-superlinear at infinity. By analyzing the solution in the interior of the unit ball as well as near the boundary, we prove that the system has no positive radially symmetric and radially decreasing solution for λ large.

Published March 27, 2023.
Math Subject Classifications: 34B18, 35B09, 35J92.
Key Words: Positive radial solution; ball; p-Laplacian system; semipositone; p-superlinear at infinity.
DOI: https://doi.org/10.58997/ejde.sp.02.a1

Show me the PDF file (346 K), TEX file for this article.

Abraham Abebe
Department of Science, Technology, Engineering & Mathematics
Delaware County Community College
PA 19122 USA
email: aabebe@dccc.edu
Maya Chhetri
Department of Mathematics and Statistics
The University of North Carolina at Greensboro
Greensboro, NC 27402 USA
email: maya@uncg.edu

Return to the table of contents for this special issue.
Return to the EJDE web page