Bound sets approach to BVPs: retrospective and perspectives

摘要: Continuation principles for the solvability of boundary value problems, depending on degree arguments, require fixed point free boundaries given sets candidate solutions (see e.g. [4]). One techniques to satisfy related transversality conditions is relied construction (Liapunov‐like) bounding functions, whence title. In our contribution, which based recent papers [5]–[8], [9], [10], we will rather demonstrate essential ideas this technique than concrete results in [10]. We also try out main difficulties and indicate how overcome them.