Global Bifurcation from Intervals for Problems with Pucci's Operator

Hua Luo; Guowei Dai

doi:10.4171/zaa/1651

JournalszaaVol. 39, No. 1pp. 67–81

Global Bifurcation from Intervals for Problems with Pucci's Operator

Hua Luo
Shanghai International Studies University, China
Guowei Dai
Dalian University of Technology, China

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Abstract

We study global bifurcation from intervals for the following fully nonlinear elliptic problem with Pucci's operator

{- M_{λ, Λ}^{+} (D^{2} u) = μu + h (u, μ) + g (u, μ) u = 0 in Ω, on \partial Ω,

where $h$ is not necessarily differentiable at the origin or infinity with respect to $u$ . Furthermore, under some suitable assumptions on nonlinearity, we investigate the global structure of bifurcating branches, which can be used to obtain the existence of one-sign solution.

Cite this article

Hua Luo, Guowei Dai, Global Bifurcation from Intervals for Problems with Pucci's Operator. Z. Anal. Anwend. 39 (2020), no. 1, pp. 67–81

DOI 10.4171/ZAA/1651