Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

Tetsutaro Shibata

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arXiv · 2309.14714

Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

Tetsutaro Shibata

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Abstract

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with oscillatory nonlinear term. We establish the precise asymptotic formulas for the bifurcation curves $\lambda(\alpha)$ as $\alpha \to \infty$ and $\alpha \to 0$, where $\alpha:= \Vert u_\lambda\Vert_\infty$ and $u_\lambda$ is the solution associated with $\lambda$. We show that the second term of $\lambda(\alpha)$ is oscillatory as $\alpha \to \infty$.

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Tetsutaro Shibata. 2023-09-26. Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term. https://arxiv.org/abs/2309.14714

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