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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
中文翻译:
黎曼流形上Yamabe型方程的整体分歧技术
更新日期:2020-09-18
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 of dimension and study positive solutions of the equation , with , . If supports a proper isoparametric function with focal varieties , of dimension we show that for any the number of positive solutions of the equation tends to as . 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 尺寸 并研究方程的正解 ,带有 , 。如果 支持具有焦点变体的适当等参函数 , 尺寸 我们证明任何 该方程的正解数 倾向于 如 。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。