4 papers · 1 filter
Stable invariant manifold for generalized ODEs with applications to measure differential equations
Weijie Lu, Paolo Piccione, Yonghui Xia
This paper establishes the stable invariant manifold for a new kind of differential equations defined by Kurzweil integral, so-called {\em generalized ODEs} on a Banach space. The…
Higher regularity of homeomorphisms in the Hartman-Grobman theorem and a conjecture on its sharpness
Weijie Lu, Manuel Pinto, Y-H Xia
Hartman-Grobman theorem states that there is a homeomorphism H sending the solutions of the nonlinear system onto those of its linearization under suitable assumptions. Many mathem…
Sharpness of conjugacy for the non-autonomous differential equations with Lipschitzian perturbation
Weijie Lu, Manuel Pinto, Y-H. Xia
The classical linearization theorem for the non-autonomous differential equations states the existence of a topological conjugacy between the nonlinear system and its l…
Higher regularity of homeomorphisms in the Hartman-Grobman theorem for semilinear evolution equations
Weijie Lu, Manuel Pinto, Y. H Xia
Hein and Prüss [J. Differential Equations, 261(2016)4709-4727] presented a version of Hartman-Grobman type linearization result for semilinear hyperbolic evolution equation…