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Global bifurcation techniques for Yamabe type equations on Riemannian manifolds
Nonlinear Analysis ( IF 1.4 ) Pub Date : 2020-09-17 , DOI: 10.1016/j.na.2020.112140
Alejandro Betancourt de la Parra , Jurgen Julio-Batalla , Jimmy Petean

We consider a closed Riemannian manifold (Mn,g) of dimension n3 and study positive solutions of the equation Δgu+λu=λuq, with λ>0, q>1. If M supports a proper isoparametric function with focal varieties M1, M2 of dimension d1d2 we show that for any q<nd2+2nd22 the number of positive solutions of the equation Δgu+λu=λuq tends to as λ+. We apply this result to prove multiplicity results for positive solutions of critical and supercritical equations. We also obtain multiplicity results for the Yamabe equation on Riemannian manifolds.



中文翻译:

黎曼流形上Yamabe型方程的整体分歧技术

我们考虑一个封闭的黎曼流形 中号ñG 尺寸 ñ3 并研究方程的正解 -ΔGü+λü=λüq,带有 λ>0q>1个。如果中号 支持具有焦点变体的适当等参函数 中号1个中号2 尺寸 d1个d2 我们证明任何 q<ñ-d2+2ñ-d2-2 该方程的正解数 -ΔGü+λü=λüq 倾向于 λ+。我们应用该结果证明了临界和超临界方程正解的多重性结果。我们还获得了黎曼流形上Yamabe方程的多重性结果。

更新日期:2020-09-18
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