partial differential equations – How do I find condition on $f$?

Find the necessary and sufficient conditions for $f in L^2(U)$ so that the equation

$sum_{i,j=1}^n (a^{ij}u_{x_i})x_j-7u=f$ in $U$ and $u=0$ on $partial U$.

has a weak solution $u in H_{0}^1(U)$.

I tried to solve this question by solving the bilinear form and Lax Milgram theorem but not able to reach the conclusion. Anyone can suggest some hints?