On the solvability of some system of integro-differential equations (Q2786053)

The authors give sufficient conditions which guarantee the existence and uniqueness of solutions of the system of integro-differential equationsNEWLINENEWLINE\[NEWLINE\sum^ n_{j=1}\frac{d}{dz}\int^ z_{\alpha}f_{ij}(z+\alpha -t)x_ j(t)dt=g_ i(z)~~~(i=1,2,\dots,n)NEWLINE\]NEWLINENEWLINEin the space \({\mathcal A(D)}\) of all holomorphic functions in a simply connected region \({\mathcal D}\) in the complex plane \(\mathbb C\). This result generalizes and improves the previous result of \textit{N. I. Nagnibida} [Sib. Math. J. 22, 748--752 (1982); translation from Sib. Mat. Zh. 22, 127--131 (1981; Zbl 0536.47029)].