Electron. J. Diff. Eqns., Vol. 2006(2006), No. 146, pp. 1-10.

On a Brezis-Nirenberg type problem

Florin Catrina

In this note we discuss the existence and symmetry breaking of least energy solutions for certain weighted elliptic equations in the unit ball in $\mathbb{R}^N$, with zero Dirichlet boundary conditions. We prove a multiplicity result, which answers one of the questions we left open in [6] regarding a Brezis-Nirenberg type problem.

Submitted February 17, 2006. Published November 26, 2006.
Math Subject Classifications: 35J25, 35J70, 35J60.
Key Words: Positive solution; ground state; symmetry breaking.

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Florin Catrina
Department of Mathematics and Computer Science
St. John's University
Queens, New York 11439, USA
email: catrinaf@stjohns.edu

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