Siberian Mathematical Journal

, Volume 42, Issue 5, pp 884–892 | Cite as

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

  • A. I. Zadorin
Article

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.

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. I. Zadorin
    • 1
  1. 1.The Institute of Applied Mathematics of the Far East Division of theKhabarovskRussian Academy of Sciences

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