Semi-hyperbolic mappings, condensing operators, and neutral delay equations

[摘要] Semi-hyperbolic mappings in Banach spaces are Lipschitz continuous and not necessarily invertible. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces; but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. It is shown that semi-hyperbolic mappings are locally psi-contracting, where psi is the Hausdorff measure of noncompactness, and that a linear operator is semi-hyperbolic if and only if it is psi-contracting and has no spectral values on the unit circle. A bishadowing result, which combines both direct and indirect forms of shadowing, is extended to semi-hyperbolic mappings in Banach spaces with locally condensing continuous comparison mappings. The result is applied to linear neutral delay equations with nonsmooth perturbations. (C) 1997 Academic Press.

[发布日期] 1997-07-01