13 citations · 42 across the 10 of their papers we have counts for
10 papers
Multiple nodal solutions having shared componentwise nodal numbers for coupled Schrödinger equations
Haoyu Li, Zhi-Qiang Wang
We investigate the structure of nodal solutions for coupled nonlinear Schrödinger equations in the repulsive coupling regime. Among other results, for the following coupled system…
Equilibrium Index of Invariant Sets and Global Static Bifurcation for Nonlinear Evolution Equations
Desheng Li, Zhi-qiang Wang
We introduce the notion of equilibrium index for statically isolated invariant sets of the system on Banach space (where is a sectorial operator with compa…
A quasilinear Schrödinger equation with Hartree type nonlinearity
Xianfa Song, Zhi-Qiang Wang
In this paper, we deal with the Cauchy problem of the quasilinear Schödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+(W(x)\ast|u|^2)u,\ x…
Global existence, blowup phenomena, and asymptotic behavior for quasilinear Schrödinger equations
Xiaowei An, Xianfa Song
In this paper, we study the Cauchy problem of the quasilinear Schrödinger equation \begin{equation*} \left\{ \begin{array}{lll} iu_t=Δu+2uh'(|u|^2)Δh(|u|^2)+F(|u|^2)u \quad {\rm fo…
Limit Behavior of Mass Critical Hartree Minimization Problems with Steep Potential Wells
Yujin Guo, Yong Luo, Zhi-Qiang Wang
We consider minimizers of the following mass critical Hartree minimization problem: \[ e_λ(N):=\underset{\{u\in H^1(R^d),\,\|u\|^2_2=N\}}{\inf} E_λ(u),\,\ d\ge 3, \] where the Hart…
Local and Global Dynamic Bifurcations of Nonlinear Evolution Equations
Desheng Li, Zhi-Qiang Wang
We present new local and global dynamic bifurcation results for nonlinear evolution equations of the form on a Banach space , where is a sectorial operator,…
Properties of ground states of attractive Gross-Pitaevskii equations with multi-well potentials
Yujin Guo, Zhi-Qiang Wang, Xiaoyu Zeng +1
We are interested in the attractive Gross-Pitaevskii (GP) equation in , where the external potential vanishes on disjoint bounded domains $Ω_i\subset \R^2\ (i=1,2,…
Infinitely many sign-changing solutions for the nonlinear Schrödinger-Poisson system
Zhaoli Liu, Zhi-Qiang Wang, Jianjun Zhang
We investigate the existence of multiple bound state solutions, in particular sign-changing solutions. By using the method of invariant sets of descending flow, we prove that this…
Bifurcations for a Coupled Schrödinger System with Multiple Components
Thomas Bartsch, Rushun Tian, Zhi-Qiang Wang
In this paper, we study local bifurcations of an indefinite elliptic system with multiple components: \begin{equation*} \left\{\begin{array}{ll} -Δu_j + au_j = μ_ju_j^3+β\sum_{k\ne…
Multiple normalized solutions for quasi-linear Schrödinger equations
Louis Jeanjean, Tingjian Luo, Zhi-Qiang Wang
In this paper we prove the existence of two solutions having a prescribed -norm for a quasi-linear Schrödinger equation. One of these solutions is a mountain pass solution rel…