Electronic Journal of Differential Equations, Vol. 2010(2010), No. 32, pp. 1-12. Title: Singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions Authors: Mohammed Bouchekif (Univ. Aboubekr Belkaid, Tlemcen, Algiria) Atika Matallah (Univ. Aboubekr Belkaid, Tlemcen, Algiria) Abstract: In this article we establish the existence of at least two distinct solutions to singular elliptic equations involving a concave term and critical Caffarelli-Kohn-Nirenberg exponent with sign-changing weight functions. Submitted September 28, 2009. Published March 03, 2010. Math Subject Classifications: 35A15, 35B25, 35B33, 35J60. Key Words: Variational methods; critical Caffarelli-Kohn-Nirenberg exponent; concave term; singular and sign-changing weights; Palais-Smale condition.