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math.AP2024
The mass-mixed case for normalized solutions to NLS equations in dimension two
Daniele Cassani, Ling Huang, Cristina Tarsi +1
\noindent We are concerned with positive normalized solutions to the following semi-linear Schrödinger equations $$ -Δu+λu=f(u), \quad\…
math.AP2024
Single-peak and multi-peak solutions for Hamiltonian elliptic systems in dimension two
Hui Zhang, Minbo Yang, Jianjun Zhang +1
This paper is concerned with the Hamiltonian elliptic system in dimension two\begin{equation*}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\…
math.AP2024
Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
Ting Deng, Marco Squassina, Jianjun Zhang +1
We are concerned with solutions of the following quasilinear Schrödinger equations \begin{eqnarray*} -{\mathrm{div}}\left(φ^{2}(u) \nabla u\right)+φ(u) φ^{\prime}(u)|\nabla u|^{2}+…