Investigation of solutions of boundary value problems for a composite type equation with non-local boundary conditions

TL;DR

This paper investigates boundary value problems for a third-order composite type equation with non-local boundary conditions, focusing on the Fredholm property and solution existence in elliptic-type models.

Contribution

It introduces a novel approach to analyze boundary value problems for third-order composite equations with non-local conditions, expanding on existing second-order models.

Findings

Analysis of Fredholm property for the boundary value problem

Conditions for existence and uniqueness of solutions

Extension of methods from second-order to third-order equations

Abstract

Since the order of elliptic type model equation (Laplace equation) is two [1], [2], then it is natural the order of composite type model equation must be [3] [4] [5] three. At each point of the domain under consideration these equations have both real and complex characteristics. Notice that a boundary value problem for a composite type equation of second order first appeared in the paper [6]. The method for investigating the Fredholm property of boundary value problems is distinctive and belongs to one of the authors of the present paper.