A short remark regarding Pohozaev-type results on general domains assuming finite Morse index. Issue 2 (16th January 2017)

• Record Type: Journal Article
• Authors: Cowan, Craig
• Is Part Of: Proceedings. Volume 147:Issue 2(2017)
• Page Start: 293
• Page End: 297
• Publication Date: 2017-01-16
• Subjects: finite Morse index, -- Pohozaev identity, -- Liouville theorems, -- Lane–Emden equation; Primary 35J61, -- 35P30; Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210516000160
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : We are interested in non-negative non-trivial solutions of where 1 < p and Ω is a bounded smooth domain in ℝ N 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.