We show that a class of divergence-form elliptic problems with quadratic
growth in the gradient and non-coercive zero order terms are solvable, under
essentially optimal hypotheses on the coefficients in the equation. In
addition, we prove that the solutions are in general not unique. The case where
the zero order term has the opposite sign was already intensively studied and
the uniqueness is the rule.Comment: To appear in Comm. PD