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Zeitschrift für Analysis und ihre Anwendungen

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Volume 39, Issue 1, 2020, pp. 67–81
DOI: 10.4171/ZAA/1651

Published online: 2020-01-24

Global Bifurcation from Intervals for Problems with Pucci's Operator

Hua Luo[1] and Guowei Dai[2]

(1) Shanghai International Studies University, China
(2) Dalian University of Technology, China

We study global bifurcation from intervals for the following fully nonlinear elliptic problem with Pucci's operator \begin{equation} \left\{ \begin{array}{ll} -\mathcal{M}_{\lambda,\Lambda}^+\left(D^2 u\right)=\mu u+h(u,\mu)+g(u,\mu)\,\,&\text{in}\,\, \Omega,\\ u=0&\text{on}\,\,\partial\Omega, \end{array} \right.\nonumber \end{equation} 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.

Keywords: Pucci's operator, interval bifurcation, one-sign solution

Luo Hua, Dai Guowei: Global Bifurcation from Intervals for Problems with Pucci's Operator. Z. Anal. Anwend. 39 (2020), 67-81. doi: 10.4171/ZAA/1651