8 papers
Uniqueness and Nondegeneracy of Ground State for the -Critical Boson Star Equation
Pan Chen, Qi Guo, Juncheng Wei +1
We prove uniqueness, up to phase rotations and translations, of the ground state for the -critical boson star equation \[ (\sqrt{-Δ}+1)Q =\bigl(|x|^{-1}* |Q|^2\bigr)Q, \qquad…
Uniqueness, Nondegeneracy, and Asymptotic Expansions of Ground States for the Dirac-Coulomb System
Pan Chen, Qi Guo, Xiaoyu Zeng
We study ground states of the following Dirac-Coulomb system $$\mathscr{D}_cu_c- \left(\abs{x}^{-1}\ast \abs{u_c}^2\right)u_c=ω_cu_c,$$ under the constraint $\norm[L^2]{u_c}^2=1.$F…
Multiplicity and Nonrelativistic limit of Bound States of Nonlinear Dirac Equations on Noncompact Metric Graphs with Localized Nonlinearities
Pan Chen, Qi Guo
In this paper, we investigate the multiplicity of normalized solutions to a nonlinear Dirac equation with localized nonlinearities on noncompact metric graphs under the \(L^2\)-con…
Existence and nonrelativistic limit of ground states to nonlinear Dirac equation
Pan Chen, Yanheng Ding, Qi Guo
This paper explores the existence and properties of ground states, including both energy and action ground states, for nonlinear Dirac equations with power-type potentials. \begin{…
Nonrelativistic Limit of Normalized Solutions to a class of nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo +1
In this paper, we investigate the nonrelativistic limit of normalized solutions to a nonlinear Dirac equation as given below: \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}…
Existence and Multiplicity of Normalized Solutions for Dirac Equations with non-autonomous nonlinearities
Anouar Bahrouni, Qi Guo, Hichem Hajaiej +1
In this paper, we study the following nonlinear Dirac equations \begin{align*} \begin{cases} -i\sum\limits_{k=1}^3α_k\partial_k u+mβu=f(x,|u|)u+ωu, \displaystyle \int_{\mathbb{R}^3…
Gradient estimates for positive weak solution to on Riemannian manifolds
Guangyue Huang, Qi Guo, Lujun Guo
In this paper, we study gradient estimates for positive weak solutions to the following -Laplacian equation on a Riemannian manifold, where and are t…
Normalized Solutions to the mixed fractional Schrodinger equations with potential and general nonlinear term
Anouar Bahrouni, Qi Guo, Hichem Hajaiej
The purpose of this paper is to establish the existence of solutions with prescribed norm to a class of nonlinear equations involving the mixed fractional Laplacians. This type of…