11 papers · 1 filter
Spectral-Edge Continuation, Dimensional Crossover, and Endpoint Stability for Partially Confined Nonlinear Schrödinger Equations
Xuexiu Zhong
We study the global geometry and endpoint dynamics of positive solutions of , , . Despite the loss of coercivity at…
Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schrödinger equations
Zhijie Chen, Youjun Wang, Jianjun Zhang +1
We study positive solutions of the partially confined stationary nonlinear Schrödinger equation $$-Δu+|y|^2u+λu=g(u),\quad (y,z)\in\mathbb{R}^d\times\mathbb{R}^{m},\quad 1\leq d<N,…
Uniqueness of radial solutions for -Laplacian equations in low dimensions
Patrizia Pucci, Jianjun Zhang, Xuexiu Zhong
This paper extends the uniqueness results of Serrin and Tang [\textit{Indiana Univ. Math. J.}, 49 (2000), pp. 897--923] to the low-dimensional case with . We c…
Multiple normalized solutions for two coupled Gross-Pitaevskii equations with attractive interactions and mass constriants
Zhang Jianjun, Zhong Xuexiu, Zhou Jinfang
We are concerned with the following system of two coupled time-independent Gross-Pitaevskii equations $$ \begin{cases} -Δu+λ_1 u=μ_1|u|^{p-2}u+να|u|^{α-2}|v|^βu ~\hbox{in}~ \R^N,\\…
Normalized solutions of coupled Sobolev critical Schrodinger equations with mass subcritical couplings
Zhang Jianjun, Zhong Xuexiu, Zhou Jinfang
We are concerned with qualitative properties of positive solutions to the following coupled Sobolev critical Schrödinger equations $$ \begin{cases} -Δu+λ_1 u=μ_1|u|^{2^*-2}u+να|u|^…
Serrin-type Overdetermination in Scaling Limits: Sharp Existence and Asymptotic Behavior of Quasi-linear Schrödinger Energy Ground States
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
This paper establishes optimal existence results and limiting profiles for energy ground states of the quasi-linear Schrödinger equation $$ -Δu - Δ(|u|^{2})u + λu = |u|^{p-2}u \qua…
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 $$ -Δu+λu=f(u), \quad\…
Single-peak and multi-peak solutions for Hamiltonian elliptic systems in dimension two
Hui Zhang, Minbo Yang, Jianjun Zhang +1
This paper is concerned with the Hamiltonian elliptic system in dimension two\begin{equation*}\aligned \left\{ \begin{array}{lll} -ε^2Δu+V(x)u=g(v)\ & \text{in}\quad \mathbb{R}^2,\…
Normalized solutions of quasilinear Schrödinger equations with a general nonlinearity
Ting Deng, Marco Squassina, Jianjun Zhang +1
We are concerned with solutions of the following quasilinear Schrödinger equations \begin{eqnarray*} -{\mathrm{div}}\left(φ^{2}(u) \nabla u\right)+φ(u) φ^{\prime}(u)|\nabla u|^{2}+…
Normalized ground states for a coupled Schrödinger system: Mass super-critical case
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We consider the existence of solutions to systems of coupled Schrödinger equations $$ \begin{cases} -Δu+λ_1 u=μ_1 u^{p…
The existence and multiplicity of solutions for general quasi-linear elliptic equations with sub-cubic nonlinearity
Chen Huang, Jianjun Zhang, Xuexiu Zhong
We consider the existence and multiplicity of solutions for a class of quasi-linear Schrödinger equations which include the modified nonlinear Schrödinger equations. A new perturba…