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 $\alpha \to \infty$.