Infinitely many sign-changing solutions for logarithmic Schrödinger equations via an \(L^p\)-perturbation approach

Chen Huang, Zhipeng Yang, Jiazheng Zhou

We study the logarithmic Schrödinger equation \[ -Δu+V(x)u=u\log u^2,\qquad x\in\mathbb R^N,\ N\ge3. \] Since the logarithmic energy is not \(C^1\) on the natural space \(H_V^1(\…