4 papers
Existence and concentration of ground state solutions for an exponentially critical Choquard equation involving mixed local-nonlocal operators
Shaoxiong Chen, Min Yang, Zhipeng Yang
We study the Choquard equation involving mixed local and nonlocal operators \[-\varepsilon^{2}Îu+\varepsilon^{2s}(-Î)^{s}u+V(x)u=\varepsilon^{μ-2}\left(\frac{1}{|x|^μ}*F(u)\rig…
Normalized Solutions and Semiclassical Concentration for Upper-Critical Fractional Choquard Equations
Yergen Aikyn, Yongpeng Chen, Michael Ruzhansky +1
We study a fractional Choquard equation with an upper-critical Hartree term, an -supercritical Hartree perturbation, and a semiclassical potential under a prescribed -mas…
Nonlinear Dirac equations on noncompact quantum graphs with potentials: Multiplicity and Concentration
Guangze Gu, Ziwei Li, Michael Ruzhansky +1
In this paper, we study the existence and multiplicity of solutions to the following class of nonlinear Dirac equations (NLDE) on noncompact quantum graphs: \[ -i\,\varepsilon c\,Ï…
Nonrelativistic limit of bound-state solutions for nonlinear Dirac equation on noncompact quantum graphs
Guangze Gu, Michael Ruzhansky, Guoyan Wei +1
In this paper, we investigate the nonrelativistic limit and qualitative properties of bound-state solutions for the nonlinear Dirac equation (NLDE) defined on noncompact quantum gr…