Asymptotic Behaviors of Chandrasekhar Variational Problem for Neutron Stars With Slater‐Type Modification.

In this paper, we consider the Chandrasekhar variational model for neutron stars with defocusing Slater‐type modifications. First, we show the existence and nonexistence of the ground state ρε$\rho _{\varepsilon }$ by concentration–compactness method, and particularly use two auxiliary functions to prove the strongly binding inequality. Second, we characterize perturbation limit behaviors of ground states ρε$\rho _{\varepsilon }$ as ε→0+$\varepsilon \rightarrow 0^+$ and obtain two different blow‐up profiles corresponding to two limit equations for N=N∗$N= N_*$ and N>N∗$N> N_*$, where ε$\varepsilon$ is a parameter corresponding to Slater‐type modifications, and N∗$N_*$ is a threshold value related to the Chandrasekhar limit. Finally, we study the limit behaviors for N≥N∗$N\ge N_*$ as ε→+∞$\varepsilon \rightarrow +\infty$, using some iterate arguments, we obtain a vanishing rate for ρε$\rho _{\varepsilon }$ that ∥ρε∥L∞≲ε−1α−1$\Vert \rho _\varepsilon \Vert _{L^\infty }\lesssim \varepsilon ^{-\frac{1}{\alpha -1}}$ as ε→+∞$\varepsilon \rightarrow +\infty$ for any 4/3<α<+∞$4/3<\alpha <+\infty$. Moreover, we characterize the limit behaviors of the energy Eε(N)$E_\varepsilon (N)$ with respect to ε$\varepsilon$, and show that limε→+∞Eε(N)=mN$\lim _{\varepsilon \rightarrow +\infty }E_\varepsilon (N)=mN$, Eε(N)$E_\varepsilon (N)$ is concave and strictly monotonically increasing with respect to ε>0$\varepsilon >0$ in some case. [ABSTRACT FROM AUTHOR]