2024/02/02 by López-Gómez, Julián, Sampedro, Juan Carlos
#35J25 #35J60 #65N06 #65P30 #Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.01519
In this paper we find out some new blow-up estimates for the positive explosive solutions of a paradigmatic class of elliptic boundary value problems of superlinear indefinite type. These estimates are obtained by combining the scaling technique of Guidas-Spruck together with a generalized De Giorgi-Moser weak Harnack inequality found, very recently, by Sirakov. In a further step, based on a comparison result of Amann and López-Gómez, we will show how these bounds provide us with some sharp a priori estimates for the classical positive solutions of a wide variety of superlinear indefinite problems. It turns out that this is the first general result where the decay rates of the potential in front of the nonlinearity a(x) do not play any role for getting a priori bounds for the positive solutions when N≥ 3.