English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We investigate the asymptotic properties of the inhomogeneous nonautonomous evolution equation (d/dt)u(t)=Au(t)+B(t)u(t)+f(t),tÃ¢ÂˆÂˆÃ¢Â„Â, where (A,D(A)) is a Hille-Yosida operator on a Banach space X,B(t),tÃ¢ÂˆÂˆÃ¢Â„Â, is a family of operators in Ã¢Â„Â’(D(A)Ã‚Â¯,X) satisfying certain boundedness and measurability conditions and fÃ¢ÂˆÂˆLÃ¢Â€Â‰locÃ¢Â€Â‰1(Ã¢Â„Â,X). The solutions of the corresponding homogeneous equations are represented by an evolution family (UB(t,s))tÃ¢Â‰Â¥s. For various function spaces Ã¢Â„Â± we show conditions on (UB(t,s))tÃ¢Â‰Â¥s and f which ensure the existence of a unique solution contained in Ã¢Â„Â±. In particular, if (UB(t,s))tÃ¢Â‰Â¥s is p-periodic there exists a unique bounded solution u subject to certain spectral assumptions on UB(p,0),f and u. We apply the results to nonautonomous semilinear retarded differential equations. For certain p-periodic retarded differential equations we derive a characteristic equation which is used to determine the spectrum of (UB(t,s))tÃ¢Â‰Â¥s

Asymptotic properties of mild solutions of nonautonomous evolution equations with applications to retarded differential equations