Linear instability of entire solutions for a class of non-autonomous elliptic equations
Published online by Cambridge University Press: 08 October 2008
Extract
We study the effect of the potential |y|α on the stability of entire solutions for elliptic equations on ℝN, N ≥ 2, with exponential or smoooth/singular polynomial nonlinearities. Instability properties are crucial in order to establish regularity of the extremal solution to some related Dirichlet nonlinear eigenvalue problem on bounded domains. As a by-product of our results, we will improve the known results about the regularity of such solutions.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 138 , Issue 5 , October 2008 , pp. 1005 - 1018
- Copyright
- Copyright © Royal Society of Edinburgh 2008
- 8
- Cited by