Morse index and symmetry-breaking bifurcation of positive solutions to the one-dimensional Liouville type equation with a step function weight

Kanako Manabe, Satoshi Tanaka

\begin{equation*} \left\{ \begin{array}{l} u'' + λh(x,α) e^u = 0, \quad x \in (-1,1), \\[1ex] u(-1) = u(1) = 0, \end{array} \right. \end{equation*} where $\lambda >0$, $0<\alpha <1$, $h(x,\alpha )=0$…