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Uniqueness of bound states to the logarithmic Schrödinger equation
Tianhao Liu, Xin Sun, Wenming Zou
This paper studies the uniqueness of bound states for the problem Δu + u\log u ^2=0, \quad u\in H^1(\RN), \quad n\geq 2, which arises from the logarithmic Schrödinger equation. We…
Dynamics of focusing nonlinear Schrödinger equation with partial harmonic confinement in higher dimensions
Tianhao Liu, Zuyu Ma, Yilin Song +1
We study the following focusing intercritical nonlinear Schrödinger equation with partial harmonic confinement: \begin{equation*} \begin{cases} i\partial_t u+Δ_{z}u-y^2 u =- |u|^αu…
Infinitely many positive solutions to nonlinear scalar field equation with nonsmooth nonlinearity
Tianhao Liu, Juncheng Wei, Wenming Zou
This paper investigates the existence of infinitely many positive solutions for the logarithmic scalar field equation \begin{equation} \tag{} \label{equ1} -Δu+ V(x) u= u\log u^2…
Multiple sign-changing and semi-nodal normalized solutions for a Gross-Pitaevskii type system on bounded domains: the -supercritical case
Tianhao Liu, Linjie Song, Qiaoran Wu +1
In this paper we investigate the existence of multiple sign-changing and semi-nodal normalized solutions for an -coupled elliptic system of the Gross-Pitaevskii type: \begin{equ…
Normalized solutions for a class of Sobolev critical Schrodinger systems
Houwang Li, Tianhao Liu, Wenming Zou
This paper focuses on the existence and multiplicity of normalized solutions for the coupled Schrodinger system with Sobolev critical coupling term. We present several existence an…
Sign-changing solution for logarithmic elliptic equations with critical exponent
Tianhao Liu, Wenming Zou
In this paper, we consider the logarithmic elliptic equations with critical exponent \begin{equation} \begin{cases} -Δu=λu+ |u|^{2^*-2}u+θu\log u^2, \\ u \in H_0^1(Ω), \quad Ω\subs…
Least energy positive soultions for -coupled Schrödinger systems with critical exponent in dimension three
Tianhao Liu, Song You, Wenming Zou
In the present paper, we consider the coupled Schrödinger systems with critical exponent: \begin{equation*} \begin{cases} -Δu_i+λ_{i}u_i=\sum\limits_{j=1}^{d} β_{ij}|u_j|^{3}|u_i|u…