Asymptotic behaviour of positive large solutions of quasilinear logistic problems

Abstract

We are interested in the asymptotic analysis of singular solutions with blow-up boundary for a class of quasilinear logistic equations with indefinite potential. Under natural assumptions, we study the competition between the growth of the variable weight and the behaviour of the nonlinear term, in order to establish the blow-up rate of the positive solution. The proofs combine the Karamata regular variation theory with a related comparison principle. The abstract result is illustrated with an application to the logistic problem with convection.

Keywords

• asymptotic behaviour; positive solution; boundary blow-up; maximum principle