35 citations · 47 across the 14 of their papers we have counts for
15 papers · 1 filter
Finite-data inverse nodal optimization in angular-momentum sectors of Schrödinger operators
Xijun Deng, Zhisu Liu, Yonghui Xia
In this paper, we study a finite-data inverse nodal optimization problem for radial Schrödinger operators in an arbitrary fixed angular-momentum sector. The analysis is built direc…
Positive radial ground states for nonlinear biharmonic equations: maximum principles and expanding-domain approximation
Daniele Cassani, Zhisu Liu, Giulio Romani +1
We prove the existence of nonnegative radial ground states for a class of nonlinear biharmonic equations in , covering subcritical and critical nonlinearities. The sol…
Orbital Stability of Smooth Traveling Solitary Waves to the Fornberg-Whitham Equation
Xijun Deng, Stephane Lafortune, Zhisu Liu
The Fornberg-Whitham (FW) equation was introduced by Fornberg and Whitham [Fornberg and Whitham, Phil. Trans. R. Soc. Lond. A (1978)] as a nonlocal model for unidirectional shallow…
Mixed-dispersion Schrödinger equations and Gagliardo-Nirenberg inequalities: equivalence between ground states and optimizers
Zhisu Liu, Giulio Romani, Yu Su
We study a nonlinear Schrödinger equation with mixed dispersion in the mass competition regime, namely mass-supercritical for the Laplacian and mass-subcritical for the Bilaplacian…
Nonlocal Schrödinger-Poisson systems in : the fractional Sobolev limiting case
Daniele Cassani, Zhisu Liu, Giulio Romani
We study the existence of positive solutions for nonlocal systems in gradient form and set in the whole . A quasilinear fractional Schrödinger equation, where the lead…
Positive solutions to the planar logarithmic Choquard equation via asymptotic approximation
Daniele Cassani, Lele Du, Zhisu Liu
In this paper we study the following nonlinear Choquard equation where …
Nonlocal planar Schrödinger-Poisson systems in the fractional Sobolev limiting case
Daniele Cassani, Zhisu Liu, Giulio Romani
We study the nonlinear Schrödinger equation for the fractional Laplacian strongly coupled with the Poisson equation in dimension two and with , which is the limi…
A new type of nodal solutions to singularly perturbed elliptic equations with supercritical growth
Zhisu Liu, Juncheng Wei, Jianjun Zhang
In this paper, we aim to investigate the following class of singularly perturbed elliptic problem $$ \left\{ \begin{array}{ll} \displaystyle -\varepsilon^2\triangle {u}+|x|^ηu =|x|…
Existence and multiplicity of sign-changing solutions for quasilinear Schrödinger equations with sub-cubic nonlinearity
Hui Zhang, Zhisu liu, Chun-Lei Tang +1
In this paper, we consider the quasilinear Schrödinger equation \begin{equation*} -Δu+V(x)u-uΔ(u^2)=g(u),\ \ x\in \mathbb{R}^{3}, \end{equation*} where and are continuous f…
Existence and multiplicity of bound state solutions to a Kirchhoff type equation with a general nonlinearity
Zhisu Liu, Haijun Luo, Jianjun Zhang
In this paper, we consider the following Kirchhoff type equation where and $f\in C(\R,…
A perturbation approach for the Schrödinger-Born-Infeld system: solutions in the subcritical and critical case
Gaetano Siciliano, Zhisu Liu
In this paper, we study the following Schrödinger-Born-infeld system with a general nonlinearity $$ \left\{ \begin{array}{ll} -\triangle u+u+ϕu=f(u)+μ|u|^4u\,\,&\mbox{in}\,\,\R^3,\…
A perturbation approach to studying sign-changing solutions of Kirchhoff equations with a general nonlinearity
Zhisu Liu, Yijun Lou, Jianjun Zhang
By employing a novel perturbation approach and the method of invariant sets of descending flow, this manuscript investigates the existence and multiplicity of sign-changing solutio…
Existence and multiplicity of sign-changing standing waves for a gauged nonlinear Schrödinger equation in
Zhisu Liu, Zigen Ouyang, Jianjun Zhang
We are concerned with sign-changing solutions of the following gauged nonlinear Schrödinger equation in dimension two including the so-called Chern-Simons term \begin{align*} \left…
Modulational stability of ground states to nonlinear Kirchhoff equations
Jianjun Zhang, Zhisu Liu, Marco Squassina
We investigate the stability of ground states to a nonlinear focusing Schrödinger equation in presence of a Kirchhoff term. Through a spectral analysis of the linearized operator a…
Ground states for fractional Kirchhoff equations with critical nonlinearity in low dimension
Zhisu Liu, Marco Squassina, Jianjun Zhang
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential . Under suitable assumptions on , using the monotonicity trick…