Abstract
Lyapunov transformations possessing certain properties are used to construct regular two-point boundary-value problems as approximations to the problem of determining a bounded solution in the general case. The concept of “limiting solutions as t→∞” is defined and the behaviour of solutions of linear ordinary differential equations as t→∞ is investigated. The necessary and sufficient conditions are derived under which a singular boundary-value problem with conditions assigned at infinity is uniquely solvable, and an appropriate approximating problem is constructed.
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