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Asymptotic behavior of ground states of generalized pseudo-relativistic Hartree equation. (arXiv:1802.03963v1 [math.AP])
来源于:arXiv
With appropriate hypotheses on the nonlinearity $f$, we prove the existence
of a ground state solution $u$ for the problem \[\sqrt{-\Delta+m^2}\,
u+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] where $V$ is a
bounded potential, not necessarily continuous, and $F$ the primitive of $f$. We
also show that any of this problem is a classical solution. Furthermore, we
prove that the ground state solution has exponential decay. 查看全文>>