Generalized Keller–Osserman conditions for fully nonlinear degenerate elliptic equations

I. Capuzzo Dolcetta^a, F. Leoni^a, A. Vitolo<sup>b

a</sup> Dipartimento di Matematica, Sapienza Università di Roma, Rome, Italy
^b Dipartimento di Ingegneria Civile, Università di Salerno, Fisciano, Italy

Abstract: We discuss the existence of entire (i.e. defined on the whole space) subsolutions of fully nonlinear degenerate elliptic equations, giving necessary and sufficient conditions on the coefficients of the lower order terms which extend the classical Keller–Osserman conditions for semilinear elliptic equations. Our analysis shows that, when the conditions of existence of entire subsolutions fail, a priori upper bounds for local subsolutions can be obtained.

UDC: 517.957

DOI: 10.22363/2413-3639-2018-64-1-74-85