LAUSR

In this paper, we shall investigate a semilinear elliptic boundary blow-up problem $$\Delta u=a(x)|u|^{p-1}u+h(x)$$ Δ u = a ( x ) | u | p - 1 u + h ( x ) in $$\Omega $$ Ω and $$u|_{\partial \Omega }=\infty $$ u | ∂ Ω = ∞ , where $$\Omega $$ Ω is a smooth bounded domain of $$\mathbb {R}^{N}$$ R N . The weight a ( x ) and the nonhomogeneous term h ( x ) may be unbounded near the boundary. Furthermore, h ( x ) may change sign and  a ( x ) may vanish in $$\Omega $$ Ω . The existence of a large solution for the problem under some assumptions on a ( x ) and h ( x ), and a consequent nonexistence result are established. We also prove the uniqueness of the solution.