  We prove the existence of a unique Malliavin differentiable strong solution
to a stochastic differential equation on the plane with merely integrable
coefficients driven by the fractional Brownian sheet with Hurst parameter
$H=(H_1,H_2)\in(0,\frac{1}{2})^2$. The proof of this result relies on a
compactness criterion for square integrable Wiener functionals from Malliavin
calculus ([Da Prato, Malliavin and Nualart, 1992]), variational techniques
developed in the case of fractional Brownian motion ([Ba\~nos, Nielssen, and
Proske, 2020]) and the concept of sectorial local nondeterminism (introduced in
[Khoshnevisan and Xiao, 2007]). The latter concept enable us to improve the
bound of the Hurst parameter (compare with [Ba\~nos, Nielssen, and Proske,
2020]).
