3 papers
math.AP2026
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(\ma…
math.AP2026
Positive normalized solutions to a singular elliptic equation with a -supercritical nonlinearity
Siyu Chen, Xiaojun Chang, Jiazheng Zhou
This paper studies the existence of positive normalized solutions to the singular elliptic equation \[ -Δu + λu = u^{-r} + u^{p-1} \quad \text{in } Ω, \] with the Dirichlet boundar…
math.AP2026
Multiple standing waves of Helmholtz equation with mixed dispersion concentrating in the high frequency limit
Shaoxiong Chen, Fei Yuan, Fukun Zhao +1
In this paper, we study the nonlinear Helmholtz equation with mixed dispersion \begin{equation*} Δ^2 u-βk^2\, Δu+αk^4 u=W(x)\, |u|^{p-2}u~\text{in}~\mathbb{R}^N, \end{equation*} wh…