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arXiv · 1802.02867

Compactly Generated Shape Index Theory and its Application to a Retarded Nonautonomous Parabolic Equation

Jintao Wang·Jinqiao Duan·Desheng Li
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Abstract

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

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Jintao Wang, Jinqiao Duan, Desheng Li. 2018-02-08. Compactly Generated Shape Index Theory and its Application to a Retarded Nonautonomous Parabolic Equation. https://arxiv.org/abs/1802.02867

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