Almost automorphic solutions of second order evolution equations

Abstract

This article is concerned with the existence of almost automorphic mild solutions to second order evolution equations of the form

where A generates a strongly continuous semigroup and f is an almost automorphic function. Using the notion of uniform spectrum of a function and the method of sums of commuting operators in previous works for the case of bounded uniformly continuous solutions, we obtain sufficient conditions for the existence of almost automorphic mild solutions to (*) in terms of spectrum of A and uniform spectrum of f. Moreover, we study the nonlinear perturbation of this equation and obtain an extension of results by Diagana and N’Guérékata.

Keywords:

• Analytic semigroup
• Almost automorphic solution
• Uniform spectrum
• Sums of commuting operators
• 1991 Mathematics Subject Classification: Primary: 34G10
• Secondary: 43A60

Notes

Email: [email protected]

Email: [email protected]

Email: [email protected]

Additional information

Notes on contributors

Nguyen Van Minh §

Email: [email protected] Email: [email protected]