Is there a solution of a first order nonlinear PDE?

Let $a^{ij}, b_{i}, c$ and $f>0$ are smooth function. Suppose $Lambda Igeq (a^{ij})geq lambda I$, where $I$ is identity matrix, $lambda, Lambda$ is positive constant. Is there solution of the following equation
$$ sum_{i,j}^{n}a^{ij}u_{i}u_{j}+sum_{i}b_{i}u_{i}+cu=f$$

on a domain $Omegasubsetmathbb{R}^{n}$ or a closed $n-$dimension manifold, where $u_{i}=frac{partial u}{partial x_{i}}$? If not, are there known condidtions ensuring that this equation admits a soulution or locally solution?