Abstract: In this paper, we use the truncation method to investigate the existence of solutions for degenerate elliptic problems with variable exponent in weighted Sobolev spaces. With the help of the Marcinkiewicz estimate and using some a priori estimates for the sequence of solutions of the approximate problem, and we choose suitable test functions for the approximate equation and obtain the needed estimates. Then, we obtain the entropy solutions for the elliptic equation in weighted Sobolev spaces with a variable exponent.

Key words: degenerate elliptic equation, weighted Sobolev space, variable exponent, truncation function