# 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?