Topological structure of solution sets to asymptotic $n$-th order vector boundary value problems

Abstract

The $R_{\delta}$-structure of solutions is investigated for asymptotic, higher-order, vector boundary value problems. Using the inverse limit technique, the topological structure is also studied, as the first step, on compact intervals. The main theorems are supplied by illustrative examples. One of them is finally applied, on the basis of our recently developed principle, to nontrivial existence problems.

Keywords

• asymptotic $n$-th order vector problems
• topological structure
• $r_{\delta}$-set
• inverse limit technique
• hukuhara–kneser–aronszajn type results