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We study the properties of solutions of fully nonlinear, positivelyhomogeneous elliptic equations near boundary points of Lipschitz domains atwhich the solution may be singular. We show that these equations have twopositive solutions in each cone of $\mathbb{R}^n$, and the solutions are uniquein an appropriate sense. We introduce a new method for analyzing the behaviorof solutions near certain Lipschitz boundary points, which permits us toclassify isolated boundary singularities of solutions which are bounded fromeither above or below. We also obtain a sharp Phragm\'en-Lindel\"of result aswell as a principle of positive singularities in certain Lipschitz domains.

Singular solutions of fully nonlinear elliptic equations and applications