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

$$
\left\{ \begin{array}{ll} -\mathcal{M}_{\lambda,\Lambda}^+\left(D^2 u\right)=\mu u+h(u,\mu)+g(u,\mu)\,\,&\text{in}\,\, \Omega,\\ u=0&\text{on}\,\,\partial\Omega, \end{array} \right.\nonumber
$$

 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.

Global Bifurcation from Intervals for Problems with Pucci's Operator

Hua Luo

Guowei Dai

Abstract

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