Some remarks on Liouville type results for quasilinear elliptic equations
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- by E. N. Dancer and Yihong Du PDF
- Proc. Amer. Math. Soc. 131 (2003), 1891-1899 Request permission
Abstract:
For a wide class of nonlinearities $f(u)$ satisfying \[ \mbox { $f(0)=f(a)=0$, $f(u)>0$ in $(0,a)$ and $f(u)<0$ in $(a,\infty )$,}\] we show that any nonnegative solution of the quasilinear equation $-\Delta _p u= f(u)$ over the entire $\mathbb {R}^N$ 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.References
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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
- 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
- © Copyright 2002 American Mathematical Society
- 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
- MathSciNet review: 1955278