In this paper, we show how to explore some properties of vector-valued pseudo S-asymptotically <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1271_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$(\omega ,c)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-periodic functions and sequences to examine the existence and uniqueness of pseudo S-asymptotically <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1271_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$(\omega ,c)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-periodic solutions to differential equations with piecewise constant arguments in Banach spaces. Pseudo S-asymptotically <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1271_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">$(\omega ,c)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>ω</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-periodic solutions considered in this paper can be unbounded and also cover bounded solutions such as pseudo S-asymptotically <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1271_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-periodic solutions, pseudo S-asymptotically <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12346_2025_1271_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega $</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation>-antiperiodic solutions and pseudo S-asymptotically Bloch periodic solutions as special cases.

New Recurrent Solutions to Differential Equations with Piecewise Constant Arguments

期刊论文
发表日期：

2025年4月5日

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Dong-Sheng Lin,
Yong-Kui Chang

摘要

In this paper, we show how to explore some properties of vector-valued pseudo S-asymptotically $(\omega ,c)$ $(ω, c)$ -periodic functions and sequences to examine the existence and uniqueness of pseudo S-asymptotically $(\omega ,c)$ $(ω, c)$ -periodic solutions to differential equations with piecewise constant arguments in Banach spaces. Pseudo S-asymptotically $(\omega ,c)$ $(ω, c)$ -periodic solutions considered in this paper can be unbounded and also cover bounded solutions such as pseudo S-asymptotically $\omega $ $ω$ -periodic solutions, pseudo S-asymptotically $\omega $ $ω$ -antiperiodic solutions and pseudo S-asymptotically Bloch periodic solutions as special cases.