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

Abstract

In this paper, we study the existence of nontrivial weak solutions to the following quasi-linear elliptic equations −△nu+V(x)|u| u= f (x,u) |x|β , x∈Rn (n>2), where−△nu=−div(|∇u|∇u), 06β<n, V :Rn→R is a continuous function, f (x,u) is continuous in Rn×R and behaves like eαu n n−1 as u →+∞. AMS Subject Classifications: 35J20, 35J60 Chinese Library Classifications: O175