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arXiv · 1802.03963

Asymptotic behavior of ground states of generalized pseudo-relativistic Hartree equation

P. Belchior·H. Bueno·O. H. Miyagaki·G. A. Pereira
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Abstract

With appropriate hypotheses on the nonlinearity $f$, we prove the existence of a ground state solution $u$ for the problem \[\sqrt{-Δ+m^2}\, u+Vu=\left(W*F(u)\right)f(u)\ \ \text{in }\ \mathbb{R}^{N},\] 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.

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P. Belchior, H. Bueno, O. H. Miyagaki, G. A. Pereira. 2018-02-12. Asymptotic behavior of ground states of generalized pseudo-relativistic Hartree equation. https://arxiv.org/abs/1802.03963

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