Formulation of problems for stationary dispersive equations of higher orders on bounded intervals with general boundary conditions

TL;DR

This paper investigates boundary value problems for higher-order stationary dispersive equations on finite intervals, establishing existence and uniqueness of solutions under general boundary conditions.

Contribution

It provides a comprehensive analysis of existence and uniqueness for linear boundary value problems of higher-order dispersive equations with general boundary conditions.

Findings

Existence of solutions is proven for the considered boundary value problems.

Uniqueness of solutions is established under general boundary conditions.

The results apply to linear stationary dispersive equations of arbitrary odd order.

Abstract

Boundary value problems for linear stationary dispersive equations of order $2l+1$, $l\in \mathbb{N}$ have been considered on finite intervals $(0,L)$. The existence and uniqueness of regular solutions have been established for general linear boundary conditions.