Integro-functional equations for solving the inverse problem for a nonlinear ordinary differential equation

We consider an inverse problem for a second-order nonlinear ordinary dierential equation with boundary conditions depending on a parameter. We prove existence and uniqueness theorems for the inverse problem by reducing it to an integro-differential equation if the original equation is autonomous and to a system of equations if the original equation is nonautonomous. Inverse problems for nonlinear ordinary differential equations were considered by numerous authors (e.g., see [1-11]). The present paper develops the results in [10, 11]. © 2005 Pleiades Publishing, Inc.