讲座内容：

We construct multi-bump positive and nodal solutions to the logarithmic scalar field equation by Lyapunov-Schmidt reduction method. The main difficulties to apply Lyapunov-Schmidt reduction to logarithmic scalar equations are caused by the non-smooth property and sublinear growth of the logarithmic nonlinearity. To overcome these difficulties, we develop a new approach to carry out the Lyapunov-Schmidt reduction, which can be used to construct not only positive but also nodal solutions to the logarithmic equations. Finally, both infinitely many positive and infinitely many nodal solutions with an arbitrarily large number of bumps are constructed for scalar field equations when the potential satisfies different proper decay conditions.