An Existence of an Isolated Solution to Nonlinear Two-Point Boundary Value Problem with Parameter

The nonlinear two-point boundary value problem with parameter for systems of ordinary differential equations is investigated by the parametrization method. The method consists in partition of the interval apart, the introduction of additional parameters and reducing the original problem to the equivalent multi-point boundary value problem with parameters. The algorithms for finding a solution to the equivalent boundary value problem are constructed. The conditions for convergence of the algorithms that ensure the solvability of nonlinear two-point boundary value problem with parameter are obtained. Definition of the isolated solution to nonlinear two-point boundary value problem with parameter, which is a modification of the well-known definition for the nonlinear two-point boundary value problem without parameter, is introduced.

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