Quasilinear elliptic equations with subquadratic growth

In this paper we consider nonlinear boundary value problems whose simplest model is the following:equation(0.1){−Δu+ν|u|p−1u=γ|∇u|2θ+f(x)inΩ,u=0on∂Ω, where f(x)f(x) is a summable function in Ω   (bounded open set in RNRN, N>2N>2), p>θ(1−θ), 0<θ<10<θ<1 and γ∈Rγ∈R.