부산대학교 도서관

Summary: ``Here, considering $-\infty < a < \frac{N-p} p$, $a \leq e \leq a + 1$, $d = 1 + a - e$ and $p^*\coloneq p^*(a, e) = \frac{N p}{N-d p}$, the existence of positive solution of a weighted $p$-Laplace equation involving vanishing potentials $$ -\Delta_{ap}u + V(x)|x|^{-ep^*} |u|^{p-2}u = |x|^{-ep^*} f (u) $$ in $\Bbb R^N$ is proved, where the potential $V$ can vanish at infinity with exponential decay and $f$ is a function with subcritical growth of class $C^1$. We use Del Pino \& Felmer's arguments to overcome the lack of compactness and the Moser iteration method with Caffarelli-Kohn-Nirenberg inequality to obtain estimates of the solution in $L^\infty(\Bbb R^N )$.