Limit behaviors of pseudo-relativistic Hartree equation with power-type perturbations

We consider the following pseudo-relativistic Hartree equations with power-type perturbation, i partial derivative(t)psi = root-Delta + m(2)psi - (1/|x| & lowast; |psi|(2))Psi + epsilon |psi|(p-2) psi, with (t, x) is an element of R x R-3 where 2 < p < 3, epsilon > 0 and m > 0, p = 8/3 can be viewed as a Slater modification. We mainly focus on the normalized ground state solitary waves phi(epsilon), where ||phi(epsilon)||(2)(2) = N . Firstly, we prove the existence and nonexistence of normalized ground states under L-2-sub critical, L-2-critical (p = 8/3) and L (2)-supercritical perturbations. Secondly, we classify perturbation limit behaviors of ground states when epsilon -> (0)+, and obtain two different blow-up profiles for N = N-c and N > N-c, where N c be regard as "Chandrasekhar limiting mass". We prove that <phi(epsilon), root- Delta phi(epsilon)>( )similar to epsilon -2/3p -4 for N = N-c and 2 < p < 3, while <phi(epsilon), root- Delta phi(epsilon)> similar to epsilon -2/3p -8 for N > N-c and 8/3 < p < 3. Finally, we study the asymptotic behavior for epsilon -> +infinity, and obtain an energy limit lim(epsilon )-> + infinity e(epsilon) (N) = 1/2 mN and a vanishing rate integral(R3) |phi(epsilon)|pdx less than or similar to epsilon(-1) when N > N-c and 8/3 < p < 3. (c) 2024 ElsevierI nc. All rights reserved