Global bifurcation curves of nonlocal elliptic equations with oscillatory nonlinear term

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 $\alpha \to \infty$.