Dirichlet problem for nonlinear higher-order equations in upper half plane. (English) Zbl 1543.30111
Summary: In this article, we consider the Dirichlet problem for nonlinear higher-order equations in upper half plane. Firstly we introduce the solutions of inhomogeneous polyanalytic equation in upper half plane. Then we investigate the properties of relevant integral operators. Lastly we transform the Dirichlet problem for nonlinear higher-order equations in upper half plane into the system of integro-differential equations and we obtain the existence of unique solution using Banach fixed point theorem.
MSC:
| 30E25 | Boundary value problems in the complex plane |
| 35G30 | Boundary value problems for nonlinear higher-order PDEs |
| 30G20 | Generalizations of Bers and Vekua type (pseudoanalytic, \(p\)-analytic, etc.) |
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