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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…