On the polynomial stability of evolution families

Abstract

The paper presents characterizations for an evolution family with the polynomial growth to be polynomially stable using the Perron method. To do this we associate the evolution family to an integral equation, which can be obtained by integrating an inhomogeneous differential equation in Banach spaces. We also give similar results of the polynomial instability by extending techniques from the polynomial stability.

Keywords:

• stability
• instability
• Perron theorem
• admissibility
• evolution family

AMS Subject Classifications:

• Primary: 34D05
• Secondary: 47D06

Acknowledgements

The authors wish to thank the referee and the editor for careful reading and valuable comments.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was completed with the support of NTU Research Scholarship.