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In this paper, we are concerned with a kind of quasilinear elliptic problems, which involves the Caffarelli-Kohn-Nirenberg inequality and critical exponents. By employing variational methods and analytical techniques, the existence of sign-changing solutions to the problem is proved. Mathematics subject classification (2010): 35J25, 35J60, 35B33.doi:10.7153/dea-02-31 fatcat:a5wfsriqxnbmtokrbyuxgjxnbm