Topological structure of solution sets to asymptotic boundary value problems (original) (raw)

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 noncompact 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.