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2022 Compactly generated shape index theory and its application to a retarded nonautonomous parabolic equation
Jintao Wang, Desheng Li, Jinqiao Duan
Topol. Methods Nonlinear Anal. 59(1): 1-33 (2022). DOI: 10.12775/TMNA.2021.031

Abstract

We establish the compactly generated shape (H-shape) index theory for local semiflows on complete metric spaces via more general shape index pairs, which allows the phase space to be not separable. The main advantages are that the quotient space $N/E$ is not necessarily metrizable for the shape index pair $(N,E)$ and $N\setminus E$ need not to be a neighbourhood of the compact invariant set. Moreover, we define H-shape cohomology groups and the H-shape cohomology index that is used to develop the Morse equations. Particularly, we apply H-shape index theory to an abstract retarded nonautonomous parabolic equation to illustrate these advantages for the new shape index theory, in which we obtain a special existence property of bounded full solutions.

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Jintao Wang. Desheng Li. Jinqiao Duan. "Compactly generated shape index theory and its application to a retarded nonautonomous parabolic equation." Topol. Methods Nonlinear Anal. 59 (1) 1 - 33, 2022. https://doi.org/10.12775/TMNA.2021.031

Information

Published: 2022
First available in Project Euclid: 23 March 2022

Digital Object Identifier: 10.12775/TMNA.2021.031

Keywords: compactly generated shape , Local semiflows , Morse equations , retarded nonautonomous equations , shape index

Rights: Copyright © 2022 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.59 • No. 1 • 2022
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