USA-Chile Workshop on Nonlinear Analysis,

Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 89-99.

### A one-dimensional nonlinear degenerate elliptic equation

Florin Catrina & Zhi-Qiang Wang

**Abstract:**

We study the one-dimensional version of the
Euler-Lagrange equation associated to finding the best constant
in the Caffarelli-Kohn-Nirenberg inequalities. We give a
complete description of all non-negative solutions which exist in a
suitable weighted Sobolev space
.
Using these results we are able to extend the parameter range for
the inequalities in higher dimensions when we consider radial
functions only, and gain some useful information about
the radial solutions in the N-dimensional case.
Published January 8, 2001.

Math Subject Classifications: 35J20, 35J70.

Key Words: best constant, ground state solutions, wighted Sobolev inequalities.

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Florin Catrina

Department of Mathematics and Statistics

Utah State University

Logan, UT 84322, USA.
Zhi-Qiang Wang

Department of Mathematics and Statistics

Utah State University

Logan, UT 84322, USA.

e-mail: wang@sunfs.math.usu.edu

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