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A short remark regarding Pohozaev-type results on general domains assuming finite Morse index

Part of: Spectral theory and eigenvalue problems Elliptic equations and systems

Published online by Cambridge University Press:  16 January 2017

Craig Cowan
Craig Cowan*
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, MB R3T 2N2, Canada (Craig.Cowan@umanitoba.ca)
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Extract

We are interested in non-negative non-trivial solutions of

where 1 < p and Ω is a bounded smooth domain in ℝN with 3 ⩽ N ⩽ 9. We show that given a non-negative integer M there is some large p(M,Ω) such that the only non-negative solution u, of Morse index at most M, is u = 0.

Keywords

finite Morse indexPohozaev identityLiouville theoremsLane–Emden equation

MSC classification

Secondary: 35J61: Semilinear elliptic equations 35P30: Nonlinear eigenvalue problems, nonlinear spectral theory
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 147 , Issue 2 , April 2017 , pp. 293 - 297
Copyright
Copyright © Royal Society of Edinburgh 2017 

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