Combined boundary value problems for the nonhomogeneous tri-analytic equation

TL;DR

This paper addresses specific boundary value problems for the inhomogeneous tri-analytic equation, developing solution methods and solvability conditions through an iterative process involving lower-order equations.

Contribution

It introduces a novel combination of boundary problems for the tri-analytic equation and provides a method to obtain solutions and solvability conditions.

Findings

Derived solutions for combined boundary problems.

Established solvability conditions for the problems.

Demonstrated the iterative approach's effectiveness.

Abstract

In the present article we present a particular combination of boundary problems for the inhomogeneous tri-analytic equation: the Neumann-(Dirichlet-Neuman) problem and the (Dirichlet-Neumann)-Dirichlet problem. In order to obtain the solution and solvability conditions we use an iteration's process involving those corresponding to equations of lower order.