Abstract
In this paper we analyze the existence and non-existence of cylindrical solutions for a nonlinear elliptic equation in ℝ3, which has been proposed as a model for the dynamics of galaxies. We prove a general integral inequality of Sobolev-Hardy type that allows us to use variational methods when the power p belongs to the interval [4, 6]. We find solutions in the range 4 < p≤ 6. The value p= 4 seems to have characteristics similar to those of the critical Sobolev exponent p= 6.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Accepted January 30, 2002¶Published online June 28, 2002
Rights and permissions
About this article
Cite this article
Badiale, M., Tarantello, G. A Sobolev-Hardy Inequality with¶Applications to a Nonlinear Elliptic Equation¶arising in Astrophysics. Arch. Rational Mech. Anal. 163, 259–293 (2002). https://doi.org/10.1007/s002050200201
Issue Date:
DOI: https://doi.org/10.1007/s002050200201