Mathematica Eterna
Open Access

Abstract

A second expansion of positive large solutions for quasilinear elliptic equations

Yun-Feng Ma, Zhong Bo Fang and Su-Cheol Yi

By means of the Karamata theory, we establish a second expansion of large solutions to the quasilinear elliptic problem ∆pu = b(x)f(u) with a singular boundary condition u|∂Ω = ∞, where the domain Ω ⊂ RN is a bounded region with C 4 -smooth boundary. The weight function b, which may vanish on the boundary, is nonnegative and nontrivial, and the function f is nonlinear and normalized regularly varying at infinity with index m.