A note on sign-changing solutions to supercritical Yamabe-type equations

2024/01/17 by Jurgen Julio-Batalla, Julio-Batalla, Jurgen · 1 citation
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Geometric Analysis and Curvature Flows #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2401.09612

Abstract

On a closed Riemannian manifold (Mⁿ ,g), we consider the Yamabe-type equation -Δ_g u + λu = λ|u|^q-1u, where λ∈ ℝ₊ and q>1. We assume that M admits a proper isoparametric function f with focal submanifolds of positive dimension. If k>0 is the minimum of the dimensions of the focal submanifolds of f, we let q^* =(n-k+2)/(n-k-2). We prove the existence of infinite f-invariant sign-changing solutions to the equation when 1

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