Higher-order stationary dispersive equations on bounded intervals: a relation between the order of an equation and the growth of its convective term

Abstract

A boundary value problem for a stationary nonlinear dispersive equation of order $2l+1l\in \mathbb{N}$ with a convective term in the form $u^k{u}_{x}k\in \mathbb{N}$ was considered on an interval $(0,L)$. The existence, uniqueness and continuous dependence of a regular solution as well as a relation between $l$ and critical values of $k$ have been established.