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