Local Bifurcation Diagrams and Degenerate Solutions of Yamabe-Type Equations

被引：0

作者：

Catalan, Sahid Bernabe ^{[1
]}

Petean, Jimmy ^{[1
]}

机构：

[1] CIMAT, Ctr Invest Matemat, Calle Jalisco S-N, Guanajuato 36023, Mexico

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2025年 / 35卷 / 04期

关键词：

Yamabe equation; Local bifurcation; Jacobi polynomials; NONLINEAR DIFFERENTIAL-EQUATIONS; ISOPARAMETRIC HYPERSURFACES; PRODUCT;

D O I：

10.1007/s12220-025-01955-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study positive solutions of the equation -Delta(g)u + lambda u = lambda u(q), with lambda > 0, q > 1 on the round sphere S-n. We reduce the equation to an ordinary differential equation by considering isoparametric functions and apply bifurcation theory. We study when the corresponding bifurcation points are transcritical. We apply this result to show the existence of degenerate solutions to the equation and to study multiplicity results for conformal constant scalar curvature metrics.

引用

页数：18

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