Large solutions for a nonhomogeneous quasilinear elliptic problem

This paper focuses on a nonhomogeneous quasilinear elliptic boundary blow up problem △pu=a(x)f(u)+h(x)inΩ,u|∂Ω=∞,where p>1, Ω is a smooth bounded domain in Rn, and h∈C(Ω) may be sign-changing in Ω and singular on ∂Ω. We mainly analyze the influences caused by h on the existence of large solutions. Furthermore, it can be verified that any large solution is nonnegative under an additional assumption.