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We prove the existence of a unique Malliavin differentiable strong solutionto a stochastic differential equation on the plane with merely integrablecoefficients 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 acompactness criterion for square integrable Wiener functionals from Malliavincalculus ([Da Prato, Malliavin and Nualart, 1992]), variational techniquesdeveloped in the case of fractional Brownian motion ([Ba\~nos, Nielssen, andProske, 2020]) and the concept of sectorial local nondeterminism (introduced in[Khoshnevisan and Xiao, 2007]). The latter concept enable us to improve thebound of the Hurst parameter (compare with [Ba\~nos, Nielssen, and Proske,2020]).

Existence of strong solutions of fractional Brownian sheet driven SDEs with integrable drift