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Bifurcation analysis of the Hardy-Sobolev equation
Journal of Differential Equations ( IF 2.4 ) Pub Date : 2021-06-22 , DOI: 10.1016/j.jde.2021.06.012
Denis Bonheure , Jean-Baptiste Casteras , Francesca Gladiali

In this paper, we prove existence of multiple non-radial solutions to the Hardy-Sobolev equation{Δuγ|x|2u=1|x|s|u|ps2u in RN{0},u0, where N3, s[0,2), ps=2(Ns)N2 and γ(,(N2)24). We extend results of E.N. Dancer, F. Gladiali, M. Grossi (2017) [12] where only the case s=0 is considered. The results specially rely on a careful analysis of the kernel of the linearized operator. Moreover, thanks to monotonicity properties of the solutions, we separate two branches of non-radial solutions.



中文翻译:

Hardy-Sobolev 方程的分岔分析

在本文中,我们证明了 Hardy-Sobolev 方程的多个非径向解的存在性{——Δ——γ|X|2=1|X|||——2 在 R。N{0},0, 在哪里 N第三名, [0,2), =2(N——)N——2 其他 γ(——,(N——2)2第四名). 我们扩展了 EN Dancer、F. Gladiali、M. Grossi (2017) [12] 的结果,其中只有=0被认为。结果特别依赖于对线性化算子内核的仔细分析。此外,由于解的单调性,我们将非径向解的两个分支分开。

更新日期:2021-06-23
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