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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 $λ(α)$ as $α\to \infty$ and $α\to 0$, where $α:= \Vert u_λ\Vert_\infty$ and $u_λ$ is the solution associated with $λ$. We show that the second term of $λ(α)$ is oscillatory as $α\to \infty$.

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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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