Abstract
We consider a bifurcation problem for a general class of fully nonlinear, second-order elliptic equations on a regular bounded domain in R n {\mathbb {R}^n} and subject to homogeneous Dirichlet boundary data. We assume that the linearized problem about the trivial solution possesses a positive solution for at least one isolated parameter value. With no other growth or sign conditions imposed upon the nonlinearity, we establish the existence of a global branch of nontrivial positive solutions. Moreover, if there is only one such isolated value of the parameter, we deduce that the branch of positive solutions is unbounded.
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