Existence and uniqueness results for large solutions of general nonlinear elliptic equations

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Singular phenomena in nonlinear elliptic problems. From blow-up boundary solutions to equations with singular nonlinearities (2006, background): “Nonlinear elliptic equation, singularity, boundary blow-up, bifurcation, asymptotic anal- ysis, maximum principle, Karamata regular variation theory.”
Existence and nonexistence of solutions for singular quadratic quasilinear equations (2009, background): “1 is an extension to quasilinear equations of the well-known local a priori estimate of Keller [24] and Osserman [33] (see also [5,31,32,37,38] and the references cited therein) for semilinear operators.”
Keller–Osserman type conditions for some elliptic problems with gradient terms (2012, background): “These cases have been also studied when the underlying domain Ω is not necessarily smooth: see [44,45,18].”
Back to the Keller-Osserman Condition for Boundary Blow-up Solutions (2007, unknown): “Extra requirements such as the convexity of f or the monotony of f ( u ) /u are needed in the proofs found in the literature (see e.g. [13]).”
On the Monge–Ampère equation with boundary blow-up: existence, uniqueness and asymptotics (2007, methodology): “admits a minimal positive C 2 (�) -solution, say u� .S ince(A3) holds, by Theorem 3.1 in [ 14 ]”