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<p>The aim of this paper is to study the remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x'=A(t)x+f(t)+F(t,x)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>A</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> <mo>+</mo> <mi>f</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>+</mo> <mi>F</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> with remotely almost periodic coefficients if the linear equation <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(x'=A(t)x\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>x</mi> <mo>′</mo> </msup> <mo>=</mo> <mi>A</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mi>x</mi> </mrow> </math></EquationSource> </InlineEquation> satisfies the condition of exponential dichotomy and the nonlinearity <i>F</i> is sufficiently “small.”</p>

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Remotely almost periodic solutions of ordinary differential equations in Banach spaces

  • 期刊论文

  • 发表日期：

    2025年12月5日

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  • David Cheban

摘要

The aim of this paper is to study the remotely almost periodic solutions of ordinary differential equations in Banach spaces of the form \(x'=A(t)x+f(t)+F(t,x)\) x ′ = A ( t ) x + f ( t ) + F ( t , x ) with remotely almost periodic coefficients if the linear equation \(x'=A(t)x\) x ′ = A ( t ) x satisfies the condition of exponential dichotomy and the nonlinearity F is sufficiently “small.”