, Volume 42, Issue 5, pp 884-892

Reduction from a Semi-Infinite Interval to a Finite Interval of a Nonlinear Boundary Value Problem for a System of Second-Order Equations with a Small Parameter

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Abstract

We consider a boundary value problem over a semi-infinite interval for a nonlinear autonomous system of second-order ordinary differential equations with a small parameter at the leading derivatives. We impose certain constraints on the Jacobian under which a solution to the problem exists and is unique. To transfer the boundary condition from infinity, we use the well-known approach that rests on distinguishing the variety of solutions satisfying the limit condition at infinity. To solve an auxiliary Cauchy problem, we apply expansions of a solution in the parameter.