A class of integral functionals with a $W^{1,1}_0$-minimum

In this paper, we study the minimization of the integral functionals of the type $$ \int\_{\Omega}\frac{|\nabla v|^2}{\big\[1+B|v|\big]^{2}} + \frac12\int\_{\Omega} a(x)|v|^2 - \frac1q\int\_{\Omega} \rho(x)|v|^q, $$ where $0\0$ the condition $|\rho(x)|\leq Q a(x)$, we show the existence of a minimum of the functional which belongs to $W\_{0}^{1,2}(\Omega){\cap L^\infty(\Omega)}\setminus{0}$.