Abstract
Topological structure is investigated for second-order vector asymptotic boundary value problems. Because of indicated obstructions, the R δ -structure is firstly studied for problems on compact intervals and then, by means of the inverse limit method, on non-compact intervals. The information about the structure is furthermore employed, by virtue of a fixed-point index technique in Fréchet spaces developed by ourselves earlier, for obtaining an existence result for nonlinear asymptotic problems. Some illustrating examples are supplied.
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