Necessary and sufficient conditions for the existence of an “isolated” solution of a nonlinear two-point boundary-value problem
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A nonlinear two-point boundary-value problem for a system of ordinary differential equations is studied by splitting the interval and introducing additional parameters. We construct a system of equations with respect to the parameters, which enable us to determine the initial approximation to the solution of the boundary-value problem. We establish necessary and sufficient conditions for the existence of an isolated solution of the analyzed problem.
KeywordsOrdinary Differential Equation Cauchy Problem Continuous Partial Derivative Unique Solvability Nonlinear Operator Equation
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