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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we investigate weighted asymptotic behavior of solutions to the Sobolev-type differential equation \begin{equation*} \frac{d}{dt}[u(t)+f(t,u(t))]=A(t)u(t)+g(t,u(t)), \ \ t\in \mathbb{R}, \end{equation*}% where $A(t) : D \subset \mathbb{X} \rightarrow \mathbb{X}$ for $t \in \mathbb{R}$ is a family of densely defined closed linear operator on a domain $D$, independent of $t$, and $f\ : \mathbb{R} \times \mathbb{X} \rightarrow \mathbb{X}$ is a weighted pseudo almost automorphic function and $g\ : \mathbb{R} \times \mathbb{X} \rightarrow \mathbb{X}$ is an $S^{p}$-weighted pseudo almost automorphic function and satisfying suitable conditions. Some sufficient conditions are established by properties of $S^{p}$-weighted pseudo almost automorphic functions combined with theories of asymptotically stable of operators.

Weighted asymptotic behavior of solutions to a Sobolev-type differential equation with Stepanov coefficients in Banach spaces