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

2018/02/12 by P. Belchior, Hamilton Bueno, Belchior, P. +5
Mathematics · #Advanced Mathematical Physics Problems #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1802.03963

Abstract

With appropriate hypotheses on the nonlinearity f, we prove the existence of a ground state solution u for the problem √(-Δ+m²) u+Vu=(W*F(u))f(u) in 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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