On explosive solutions for a class of quasi-linear elliptic equations

We study existence, uniqueness, multiplicity and symmetry of large solutions for a class of quasi-linear elliptic equations. Furthermore, we characterize the boundary blow-up rate of solutions, including the case where the contribution of boundary curvature appears.Comment: 34 page

A new critical curve for a class of quasilinear elliptic systems

We study a class of systems of quasilinear differential inequalities associated to weakly coercive differential operators and power reaction terms. The main model cases are given by the $p$-Laplacian operator as well as the mean curvature operator in non parametric form. We prove that if the exponents lie under a certain curve, then the system has only the trivial solution. These results hold without any restriction provided the possible solutions are more regular. The underlying framework is the classical Euclidean case as well as the Carnot groups setting.Comment: 28 page

Asymptotic behaviour of positive large solutions of quasilinear logistic problems

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