Electronic Journal of Differential Equations, Vol. 2012 (2012), No. 120, pp. 1-14. Title: Solutions of p(x)-Laplacian equations with critical exponent and perturbations in R^N Authors: Xia Zhang (Harbin Inst. of Technology, Harbin, China) Yongqiang Fu (Harbin Inst. of Technology, Harbin, China) Submitted Submitted June 19, 2012. Published July 19, 2012. Math Subject Classifications: 35J60, 46E35. Key Words: Variable exponent Sobolev space; critical exponent; weak solution.