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Large spectral gap induced by small delay and its application to reduction

This work was partly supported by NSFC grant (No.11831012), the Fundamental Research Funds for the Central Universities (No.YJ201646), International Visiting Program for Excellent Young Scholars of SCU

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  • We consider general linear neutral differential equations with small delays in the view of pseudo exponential dichotomy. For the autonomous case, we first count the eigenvalues in a certain half plane, which generalized the previous works on serval special retarded differential equations. We next establish the existence of a pseudo exponential dichotomy for the nonautonomous case, and prove that the corresponding spectral gap approaches infinity as the delay tends to zero. The proof for this large spectral gap induced by small delay is owing to exact bounds and exponents for pseudo exponential dichotomy. Then based on above results, we give an invariant manifold reduction theorem for nonlinear neutral differential equations with small delays. Finally, our results are applied to a concrete example.

    Mathematics Subject Classification: Primary: 34K06; Secondary: 34D09, 34K19.


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