Existence and Uniqueness Theorem for a Solution to a Class of a Third-Order Nonlinear Differential Equation in the Domain of Analyticity

The paper considers the specifics of nonlinear differential equations that have applications in different areas. Earlier, the authors proved the existence and uniqueness theorem for a solution to a class of non-linear differential equations in a neighborhood of a moving singular point. In this paper, we consider the first problem of studying a third-order nonlinear differential equation in the domain of analyticity. An analytical approximate solution is built, taking into account the solution search area. A priori estimates of the analytical approximate solution are obtained, and the technology of their optimization using a posteriori ones is illustrated. The result of a numerical experiment is presented. The presented results allow to expand the class of nonlinear differential equations for describing various phenomena and processes.