Several boundary value problems for bi-analytic complex partial differential systems of second order

In this paper, several boundary value problems for second order complex partial differential systems of bi-analytic functions were investigated on the bicylinder. Homogeneous and nonhomogeneous Dirichlet problems for $(\lambda ,1)$ bi-analytic functions were first discussed on the bicylinder. Applying the Cauchy-Pompeiu formula and the properties of the Poisson kernel, the expressions of the solutions to the Dirichlet problems were obtained. Thereafter, the Riemann problems and the inverse problems for $(\lambda ,1)$ bi-analytic functions were explored on the generalized bicylinder in ${\mathbb{C}}^2$. Applying the Plemelj formula, the solutions to the corresponding problems were obtained.