Contemporary Mathematics. Fundamental DirectionsContemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направления2413-36392949-0618Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)2226210.22363/2413-3639-2018-64-1-74-85New ResultsНовые результатыResearch ArticleGeneralized Keller-Osserman Conditions for Fully Nonlinear Degenerate Elliptic EquationsОбобщенные условия Келлера-Оссермана для полностью нелинейных вырождающихся эллиптических уравненийCapuzzo DolcettaIКапуццо ДольчеттаИcapuzzo@mat.uniroma1.itLeoniFЛеониФleoni@mat.uniroma1.itVitoloAВитолоАvitolo@unisa.itSapienza Universita` di RomaUniversita` di Salerno15122018641Differential and Functional Differential EquationsДифференциальные и функционально-дифференциальные уравнения748529112019Copyright ©; 2019, Contemporary Mathematics. Fundamental DirectionsCopyright ©; 2019, Современная математика. Фундаментальные направления2019Contemporary Mathematics. Fundamental DirectionsСовременная математика. Фундаментальные направленияhttps://journals.rudn.ru/CMFD/article/view/22262We 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.Исследуется существование глобальных (т. е. определенных на всем пространстве) субрешений полностью нелинейных вырождающихся эллиптических уравнений. Необходимые и достаточные условия на коэффициенты при младших членах обобщают классические условия Келлера- Оссермана для полулинейных эллиптических уравнений. 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