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In this paper we study a Dirichlet problem for an elliptic equation with degenerate coercivity and a singular lower order term with natural growth with respect to the gradient. The model problem is 1991 Mathematics Subject Classification. 35J15, 35J25, 35J66, 35J70, 35J75.doi:10.3934/dcdss.2012.5.507 fatcat:tu3hl3zlyfc7xj6sk4vpegoybu