58 citations · 151 across the 20 of their papers we have counts for
22 papers
Bifurcation from essential spectrum for an elliptic equation with general nonlinearity
Jianjun Zhang, Xuexiu Zhong, Huansong Zhou
In this paper, based on some prior estimates, we show that the essential spectrum is a bifurcation point for an superlinear elliptic equation with only local conditions, whic…
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|…
On the Kirchhoff equation with prescribed mass and general nonlinearities
Xiaoyu Zeng, Jianjun Zhang, Yimin Zhang +1
In the present paper, we apply a global branch approach to study the existence, non-existence and multiplicity of positive normalized solutions $(λ_c, u_c)\in \mathbb{R}\times H^1(…
A global branch approach to normalized solutions for the Schrödinger equation
Louis Jeanjean, Jianjun Zhang, Xuexiu Zhong
We study the existence, non-existence and multiplicity of prescribed mass positive solutions to a Schrödinger equation of the form \begin{equation*} -Δu+λu=g(u), \quad u \in H^1(\m…
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 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…
Bose fluids and positive solutions to weakly coupled systems with critical growth in dimension two
Daniele Cassani, Hugo Tavares, Jianjun Zhang
We prove, using variational methods, the existence in dimension two of positive vector ground states solutions for the Bose-Einstein type systems \begin{equation} \begin{cases} -Δu…
Solutions concentrating around the saddle points of the potential for Schrödinger equations with critical exponential growth
J. Zhang, J. M. do Ó, P. K. Mishra
In this paper, we deal with the following nonlinear Schrödinger equation where has critical growth of Trudinger-Moser type.…
Groundstates for Choquard type equations with Hardy-Littlewood-Sobolev lower critical exponent
Daniele Cassani, Jean Van Schaftingen, Jianjun Zhang
For the Choquard equation, which is a nonlocal nonlinear Schrödinger type equation, , in where $N\g…
Existence and concentration of positive solutions for nonlinear Kirchhoff type problems with a general critical nonlinearity
Jianjun Zhang, David G. Costa, João Marcos Do Ó
We are concerned with the following Kirchhoff type equation $$-\varepsilon^2 M \left(\varepsilon^{2-N} \int_{\mathbb{R}^N} | \nabla u|^2\, \mathrm{d} x\right) Δu+V(x)u = f(u),\ x \…
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…
Ground states and semiclassical states of nonlinear Choquard equations involving Hardy-Littlewood-Sobolev critical growth
Daniele Cassani, Jianjun Zhang
We are concerned with the existence of ground states for nonlinear Choquard equations involving a critical nonlinearity in the sense of Hardy-Littlewood-Sobolev. Our result complem…
Singularly perturbed fractional Schrödinger equation involving a general critical nonlinearity
Hua Jin, Wenbin Liu, Jianjun Zhang
In this paper, we are concerned with the existence and concentration phenomena of solutions for the following singularly perturbed fractional Schrödinger problem \begin{align*} \va…
A priori estimates and positivity for semiclassical ground states for systems of critical Schroedinger equations in dimension two
Daniele Cassani, Jianjun Zhang
We consider in the whole plane the Hamiltonian coupling of semilinear Schroedinger equations which have critical growth in the sense of Moser. We prove that the (nonempty) set S of…
Multi-peak solutions for nonlinear Choquard equation with a general nonlinearity
Minbo Yang, Jianjun Zhang, Yimin Zhang
In this paper, we study a class of nonlinear Choquard type equations involving a general nonlinearity. By using the method of penalization argument, we show that there exists a fam…
Fractional Schrödinger-Poisson systems with a general subcritical or critical nonlinearity
Jianjun Zhang, João Marcos do Ó, Marco Squassina
We consider a fractional Schrödinger-Poisson system with a general nonlinearity in subcritical and critical case. The Ambrosetti-Rabinowitz condition is not required. By using a pe…
Schrödinger-Poisson systems with a general critical nonlinearity
Jianjun Zhang, João Marcos do Ó, Marco Squassina
We consider a Schrödinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition i…
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…
Standing Waves for nonlinear Schrodinger Equations involving critical growth
Jianjun Zhang, Zhijie Chen, Wenming Zou
We consider the following singularly perturbed nonlinear elliptic problem: $$-\e^2Δu+V(x)u=f(u),\ u\in H^1(\mathbb{R^N}),$$ where and the nonlinearity is of critical g…