Electronic Journal of Differential Equations, Vol. 2015 (2015), No. 84, pp. 1-11. Title: Ground state solutions for semilinear elliptic equations with zero mass in R^N Authors: Jiu Liu (Southwest Univ., Chongqing, China) Jia-Feng Liao (Southwest Univ., Chongqing, China) Chun-Lei Tang (Southwest Univ., Chongqing, China) Abstract: In this article, we study the semilinear elliptic equation $$\displaylines{ -\Delta u=|u|^{p(x)-2}u, \quad x\in \mathbb{R}^N\cr u\in D^{1,2}(\mathbb{R}^N), }$$ where $N\geq3$, $p(x)=\begin{cases} p, &x\in\Omega\\ 2^*, &x\not\in\Omega, \end{cases}$ with $2