Existence of Large Solutions for Quasilinear Elliptic Equation - Li, Xiao; Yang, Zuodong (Communications in Mathematics and Applications, 2011)
In this paper, we consider the problem align*cases-div(| abla u|^p-2 abla u)=λ u-b(x)h(u),&xΩ u=+∞, &on Ω.casesalign*where Ω is a smooth bounded domain in R^N. The weight function b(x) is a non-negative continuous function in the domain, h(u) is locally Lipschitz continuous, h(u)/u^p-1 is increasing on (0,∞) and h(u)Hu^m(p-1) for sufficiently large u with H>0 and m>1. We establish conditions sufficient to ensure the existence of positive large solutions of the equation.