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math.AP2024
A New Approach to Solving Singularly Perturbed NLS at Local Potential Maxima
Chengxiang Zhang
This paper presents a new approach for addressing the singularly perturbed nonlinear Schrödinger (NLS) equation: \begin{equation} -\varepsilon^2Δv + V(x) v =f(v),\ v>0,\ \lim_{|x|\…
math.AP2017
Remarks on the Clark theorem
Guosheng Jiang, Kazunaga Tanaka, Chengxiang Zhang
The Clark theorem is important in critical point theory. For a class of even functionals it ensures the existence of infinitely many negative critical values converging to and…
math.AP2016★ 1 cited
Multi-bump solutions for logarithmic Schrödinger equations
Kazunaga Tanaka, Chengxiang Zhang
We study spatially periodic logarithmic Schrödinger equations: \begin{equation}\tag{LS} -Δu + V(x)u=Q(x)u\log u^2, \quad u>0\quad \text{in}\ \mathbb{R}^N, \end{equation} where $N\g…