Special Issue in honor of John W. Neuberger. Electron. J. Diff. Eqns., Special Issue 02 (2023), pp. 231-238.

Existence of positive global radial solutions to nonlinear elliptic systems

Seshadev Padhi, Julio G. Dix

Abstract:
In this article we obtain global positive and radially symmetric solutions to the system of nonlinear elliptic equations

and in particular to Laplace's equation

where $j=1,\dots,k$, $ x\in\mathbb{R}^N$, $N\geq 3$, $\Delta $ is the Laplacian operator, and $\nabla$ is the gradient. Also we state conditions for solutions to be bounded, and to be unbounded. With an example we illustrate our results.

Published March 27, 2023.
Math Subject Classifications: 35J25, 45F10, 35B08.
Key Words: Radial solution; elliptic system.
DOI: https://doi.org/10.58997/ejde.sp.02.p1

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Seshadev Padhi
Department of Mathematics
Birla Institute of Technology
Mesra Ranchi, India
email: spadhi@bitmesra.ac.in
Julio G. Dix
Department of Mathematics
Texas State University
601 University Drive
San Marcos, TX 78666, USA
email: jd01@txstate.edu

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