Some remarks on elliptic problems with critical growth in the gradient

In this work we analyze existence, nonexistence, multiplicity and regularity of solution to problemequation(1)-Δu=β(u)|∇u|2+λf(x)inΩ,u=0on∂Ωwhere ββ is a continuous nondecreasing positive function and ff belongs to some suitable Lebesgue spaces.