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<p>We study the one-dimensional nonlocal Kirchhoff type bifurcation problem related to logistic equation of population dynamics. We establish the precise asymptotic formulas for bifurcation curve <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math> <mi>λ</mi> <mo>=</mo> <mi>λ</mi> <mo stretchy="false">(</mo> <mi>α</mi> <mo stretchy="false">)</mo> </math></EquationSource> <EquationSource Format="TEX">$\lambda = \lambda (\alpha )$</EquationSource> </InlineEquation> as <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo stretchy="false">→</mo> <mi mathvariant="normal">∞</mi> </math></EquationSource> <EquationSource Format="TEX">$\alpha \to \infty $</EquationSource> </InlineEquation> in <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math> <msup> <mi>L</mi> <mn>2</mn> </msup> </math></EquationSource> <EquationSource Format="TEX">$L^{2}$</EquationSource> </InlineEquation>-framework, where <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math> <mi>α</mi> <mo>:</mo> <mo>=</mo> <msub> <mrow> <mo stretchy="false">∥</mo> <msub> <mi>u</mi> <mi>λ</mi> </msub> <mo stretchy="false">∥</mo> </mrow> <mn>2</mn> </msub> </math></EquationSource> <EquationSource Format="TEX">$\alpha := \Vert u_{\lambda }\Vert _{2}$</EquationSource> </InlineEquation>.</p>

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Asymptotic behavior of bifurcation curves of nonlocal logistic equation of population dynamics

  • 期刊论文

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  • 发表日期：

    2025年12月3日

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  • Tetsutaro Shibata

摘要

We study the one-dimensional nonlocal Kirchhoff type bifurcation problem related to logistic equation of population dynamics. We establish the precise asymptotic formulas for bifurcation curve λ = λ ( α ) $\lambda = \lambda (\alpha )$ as α → ∞ $\alpha \to \infty $ in L 2 $L^{2}$ -framework, where α : = ∥ u λ ∥ 2 $\alpha := \Vert u_{\lambda }\Vert _{2}$ .