Pairs of positive radial solutions for a Minkowski-curvature Neumann problem with indefinite weight

2019/12/24 by Boscaggin, Alberto, Feltrin, Guglielmo · 1 citation
#34B08 #34B18 #35B09 #47H11 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1912.12205

Abstract

We prove the existence of a pair of positive radial solutions for the Neumann boundary value problem \begincases div \Biggl( \dfrac∇ u√1- | ∇ u |²\Biggr) + λa(|x|)u^p = 0, amp; in B,
∂_νu=0, amp; on ∂ B, \endcases where B is a ball centered at the origin, a(|x|) is a radial sign-changing function with ∫_B a(|x|) dx < 0, p>1 and λ> 0 is a large parameter. The proof is based on the Leray-Schauder degree theory and extends to a larger class of nonlinearities.

Cited by

• Global Leray-Schauder continuation for Fredholm operators

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