Global structure of radial sign-changing solutions for the prescribed mean curvature problem in a ball

2014/09/18 by Ruyun Ma, Ma, Ruyun, Hongliang Gao +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1409.5348

arXiv admin note: substantial text overlap with arXiv:1409.0070

arxiv created 2014/09/18 · arxiv updated 2014/09/19

Abstract

In this paper, we are concerned with the global structure of radial solutions, with prescribed nodal properties, to the boundary value problem div(ϕ_N(∇ v))+λf(|x|, v)=0 ~~~in ~~B(R), ~~~ v=0 ~~~on ~~∂ B(R), where ϕ_N(y)=\fracy√1-|y|², y∈ ℝ^N, λ is a positive parameter, B(R)=\x∈ ℝ^N :|x|<R\, and |⋅| denote the Euclidean norm in ℝ^N. All results, depending on the behavior of nonlinear term f near 0, are obtained by using global bifurcation techniques.

Citations

• Global structure of radial positive solutions for a prescribed mean curvature problem in a ball

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