Keller–Osserman type conditions for some elliptic problems with gradient terms

On the inequality $$F(x,D^2u)\ge f(u) +g(u)\, |Du|^q$$ F ( x , D 2 u ) ≥ f ( u ) + g ( u ) | D u | q

“…Alarcón et al [1] and Felmer et al [19] for fully nonlinear uniformly elliptic equations with purely first order terms of the form h(|Du|). Moreover, some results obtained by Porretta [34] on the existence of entire solutions of the equation…”

Boundary behavior of large solutions to the Monge–Ampère equations with weights

“…Since then many papers have been dedicated to resolving existence, uniqueness and asymptotic behavior issues for solutions to problem (1.3), see, for instance, [1,2,10,11,[14][15][16]27,43,47] and the references therein. Now let us return to problem (1.1).…”

Boundary behavior of large viscosity solutions to infinity Laplace equations

“…Problem (1.4) arises from many branches of mathematics and applied mathematics and has been discussed by many authors and in many contexts, see, for instance, [1,3,7,13,[16][17][18]23,25,[31][32][33][34][35][36]39,42,44,45,49,50] and the references therein. For b ≡ 1 in Ω: when f (u) = e u and N = 2, problem (1.4) was studied much earlier.…”