Some remarks on Liouville type results for quasilinear elliptic equations

Authors:
E. N. Dancer and Yihong Du

Journal:
Proc. Amer. Math. Soc. **131** (2003), 1891-1899

MSC (2000):
Primary 35J15, 35J60

DOI:
https://doi.org/10.1090/S0002-9939-02-06733-3

Published electronically:
November 4, 2002

MathSciNet review:
1955278

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Abstract | References | Similar Articles | Additional Information

Abstract: For a wide class of nonlinearities satisfying

we show that any nonnegative solution of the quasilinear equation over the entire must be a constant. Our results improve or complement some recently obtained Liouville type theorems. In particular, we completely answer a question left open by Du and Guo.

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Additional Information

**E. N. Dancer**

Affiliation:
School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia

Email:
normd@maths.usyd.edu.au

**Yihong Du**

Affiliation:
School of Mathematics, Statistics and Computer Science, University of New England, Armidale, New South Wales 2351, Australia

Email:
ydu@turing.une.edu.au

DOI:
https://doi.org/10.1090/S0002-9939-02-06733-3

Keywords:
Quasilinear elliptic equation,
Liouville theorem,
sweeping principle

Received by editor(s):
February 8, 2002

Published electronically:
November 4, 2002

Additional Notes:
The work of the first author was partially supported by the Australian Research Council

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2002
American Mathematical Society