Existence, non-existence and asymptotic behaviour of blow-up entiresolutions of quasi-linear elliptic equation

摘要

Existence, non-existence and asymptotic behaviour of blow-up entire solutionsof a class of quasi-linear elliptic equation div(|u|~(p-2)u)= p(x)f(u),x∈R~Nisobtained. Under several hypotheses on the p(x) and fir), we obtain the existenceof blow-up entire solution. Existence and asymptotic behaviour is discussed byconstructing lower and upper solution. For non-existence we explore radialsymmetry, estimates on an associated integral equation and Keller–Ossermancondition. The results of this article are new and extend previously known results.