On a Solution of a Nonlinear Semi-periodic Boundary Value Problem for a Differential Equation with Arbitrary Functions

Abstract

In this paper we consider a nonlinear semi-periodic boundary-value problem for a partial differential equation. By means of a replacement, the nonlinear problem is reduced to a linear semi-periodic boundary-value problem for hyperbolic equations with a mixed derivative. To solve the obtained problem, partitioning by the first variable is made. Further, in the obtained domains, the parametrization method proposed in the works of D.S. Dzhumabaev for solving a two-point boundary value problem for an ordinary differential equation is applied. A new algorithm for finding the solution to the given problem is proposed. Sufficient conditions for the unique solvability of a semi-periodic boundary-value problem with arbitrary functions for a nonlinear partial differential equation are established.