A note on bifurcations of \(u^{\prime\prime}+\mu (u-u^k)=0\) \((4 \leq k\in \mathbb{Z}^+)\)
Consider the boundary value problem \((*)\) \(u'' + \mu (u-u^k)=0\), \(u(0)=u(\pi)=0\), where \(\mu\) is a real parameter, \(4 \leq k \in \mathbb{Z}^+\). The author applies the Lyapunov-Schmidt method to \((*)\) and studies the corresponding bifurcation equation.
scientific article; zbMATH DE number 1490815