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arxiv: 1401.4549 · v1 · pith:OG34CU76new · submitted 2014-01-18 · 🧮 math.AP

Non-stability of Paneitz-Branson equations in arbitrary dimensions

classification 🧮 math.AP
keywords equationpaneitz-bransonarbitraryassumingcompactconditionscriticaldimension
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Let $(M,g)$ be a compact riemannian manifold of dimension $n\geq 5$. We are interested in the stability of a slighly subcritical Paneitz-Branson type equation on $M$. Assuming that there exists a positive nondegenerate solution of the critical equation and under suitable conditions, we prove that this equation is not stable for all $n\geq 5$.

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