Sufficient conditions for the existence of an isolated solution to a nonlocal boundary value problem for a nonlinear third-order pseudoparabolic equation

Abstract

In this paper, a third-order nonlinear pseudo-parabolic equation with nonlocal boundary conditions is studied. The original boundary value problem is reduced to a multicharacteristic nonlinear boundary value problem with functional parameters. Subsequently, the resulting problem is transformed into a system of integro-differential equations, which enables the proposal of an iterative algorithm for finding the solution. Sufficient conditions for the existence, uniqueness, and convergence of the solution are established. It is proved that the sequence of approximations generated by this algorithm converges to an isolated solution of the problem.