An ODE reduction method for the semi-Riemannian Yamabe problem on space forms

نویسندگان

چکیده

We consider the semi-Riemannian Yamabe type equations of form −□u+λu=μ|u|p−1uonMwhere M is either semi-Euclidean space or pseudosphere dimension m≥3, □ Laplacian in M, λ≥0, μ∈R∖︀{0} and p>1. Using isoparametric functions on we reduce PDE into a generalized Emden–Fowler ODE w′′+q(r)w′+λw=μ|w|p−1wonI,where I⊂R [0,∞) [0,π], q(r) blows-up at 0 w subject to natural initial conditions w′(0)=0 first case w′(0)=w′(π)=0 second. prove existence blowing-up globally defined solutions this problem, both positive sign-changing, inducing problem with same qualitative properties, level critical sets described terms hypersurfaces focal varieties. In particular, sign-changing having prescribed number nodal domains.

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ژورنال

عنوان ژورنال: Nonlinear Analysis-theory Methods & Applications

سال: 2021

ISSN: ['1873-5215', '0362-546X']

DOI: https://doi.org/10.1016/j.na.2021.112342