Degenerate elliptic equations with a natural growth gradient term and a strongly increasing lower term

We study the existence and regularity of solutions for elliptic equations with degenerate coercivity and with both a natural growth term depending on the gradient and a strongly increasing lower term. The source term $f$ belongs to $L^{m}(\Omega )$ with $m \geq 1$. Moreover, we show a regularizing for effect solutions.