| Summary: | In this article, we consider degenerate and singular elliptic systems of the form $$displaylines{ - hbox{div}(h_1(x)abla u) = b_1(x)|u|^{r-2}u + F_u(x,u,v) quad hbox{in } Omega,cr - hbox{div}(h_2(x)abla v) = b_2(x)|v|^{r-2}v + F_v(x,u,v) quad hbox{in } Omega, }$$ where $Omega$ is a bounded domain in $mathbb{R}^N$, $N geq 2$, with smooth boundary $partialOmega$; $h_i: Omega o [0, infty)$, $h_i in L^1_{loc}(Omega)$, and are allowed to have ``essential'' zeroes; $1 < r < 2$; the weight functions $b_i: Omega o mathbb{R}$, may be sign-changing; and $(F_u,F_v) = abla F$. Using variational techniques, a variant of the Caffarelli - Kohn - Nirenberg inequality, and a variational principle by Clark [9], we prove the rxistence of infinitely many solutions in a weighted Sobolev space.
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