Norm localization and nonexistence for one-dimensional Kirchhoff equations

We consider the one-dimensional Kirchhoff equation [Formula: see text] subject to the right-focal boundary data [Formula: see text] We demonstrate that this problem has no solution for all [Formula: see text] sufficiently large when certain conditions are imposed on the functions [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. Due to the convolutional structure, a variety of nonlocal coefficients are included in our results, including Caputo fractional derivatives. Our results rely on a careful analysis of the quantity [Formula: see text]. As part of this analysis we analyze the topological structure of certain subsets of [Formula: see text] related to solutions of the differential equation.