Solvability of Uniformly Elliptic Fully Nonlinear PDE

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Existence and Multiplicity for Elliptic Problems with Quadratic Growth in the Gradient (2010, background): “As far as Theorem 2 is concerned, the fact that in problems with natural growth in the gradient the presence of a non-coercive zero-order term may lead to nonuniqueness of bounded solutions was observed only very recently in [24], for the equation (2.”
Nonexistence of Positive Supersolutions of Elliptic Equations via the Maximum Principle (2010, background): “Condition (1.3) appeared first in Ni and Serrin [35], where the nonexistence of decaying radial solutions to some quasilinear inequalities like − pu ≥ x − u in n for ≤ n− p− 1 / n− p was proved.”