On the existence of positive solutions for a class of semilinear elliptic equations Original Research Article

We prove some existence and nonexistence results for the semilinear elliptic equation Δu=q(x)f(u) on View the MathML source where u is required to blow up on the boundary of Ω and f is a nonnegative function which is assumed to be Lipschitz continuous and bounded away from zero on each interval [ε,∞) and have at worst linear growth. In particular, we extend some results already obtained in the case where f(u)=uγ, 0<γ⩽1.