Exact solutions and bifurcation curves of nonlocal elliptic equations with convolutional Kirchhoff functions

We study the one-dimensional nonlocal elliptic equation of Kirchhoff type with convolutional Kirchhoff functions. We establish the exact solutions $u_{\lambda }$ and bifurcation curves $\lambda (\alpha )$, where $\alpha :=\mathrm{\parallel }{u}_{\lambda }{\mathrm{\parallel }}_{\mathrm{\infty }}$.