Existence of Nontrivial Weak Solutions to Quasi-Linear Elliptic Equations with Exponential Growth

摘要

In this paper,we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations -△nu+V(x)｜u｜n-2u-f(x,u)/｜x｜β,x∈Rn (n≥2),where-△nu=-div(｜▽u｜n-2▽7u),0≤β ＜ n,V∶ Rn → R is a continuous function,f (x,u)is continuous in Rn × R and behaves like eαun-1 as u → +∞.