Abstract: In this paper, we get the L^∞ estimate for the solutions of the following elliptic equation in R^N with limiting Sobolev exponent and inhomogeneous term
-∑i₌₁^N(∂)/∂xⁱ(|▽u|^p-2(∂u)/∂xⁱ)+c(x)|u|^p-2u=f(x,u)+g(x),u∈R^N,u∈W^1,p(R^N),N > p > 1 and we show that any solution u of the above equation satisfies
||u||_{∞(|x| ≥ R)} ≤ C||u||_p^τ·_{(|x| ≥ (1)/2R)}.