  We prove a comparison theorem for super- and sub-solutions with non-vanishing
gradients to semilinear PDEs provided a nonlinearity $f$ is $L^p$ function with
$p > 1$. The proof is based on a strong maximum principle for solutions of
divergence type elliptic equations with VMO leading coefficients and with lower
order coefficients from a Kato class. An application to estimation of periodic
water waves profiles is given.
