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<p>In this paper, we study the existence of periodic solutions for Duffing equations <Equation ID="Equa"> <EquationSource Format="TEX">\(x^{\prime\prime}+g(t, \, x) = 0.\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msup> <mi>x</mi> <mrow> <mi class="MJX-variant" mathvariant="normal">′</mi> <mi class="MJX-variant" mathvariant="normal">′</mi> </mrow> </msup> <mo>+</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>t</mi> <mo>,</mo> <mspace width="thinmathspace" /> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mn>0</mn> <mo>.</mo> </math></EquationSource> </Equation></p><p>We give a Landesman-Lazer type condition for the existence of periodic solutions of the given equation when <i>g</i> satisfies one-sided superlinear condition and one-sided resonant condition.</p>

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Periodic Solutions of Duffing Equations under One-sided Resonant Conditions

  • 期刊论文

  • 发表日期：

    2026年7月7日

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  • Cong-min Yang,
  • Zai-hong Wang

摘要

In this paper, we study the existence of periodic solutions for Duffing equations \(x^{\prime\prime}+g(t, \, x) = 0.\) x ′ ′ + g ( t , x ) = 0 .

We give a Landesman-Lazer type condition for the existence of periodic solutions of the given equation when g satisfies one-sided superlinear condition and one-sided resonant condition.