Results on a strongly coupled, asymptotically linear pseudo-relativistic Schrödinger system : ground state, radial symmetry and Hölder regularity.
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Date
2022
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Abstract
In this paper we consider the asymptotically linear, strongly coupled nonlinear
system
⎧
⎪⎨
⎪⎩
√
−∆ + m2 u =
u
2 + v
2
1 + s(u2 + v
2)
u + λv,
√
−∆ + m2 v =
u
2 + v
2
1 + s(u2 + v
2)
v + λu,
where m > 0, 0 < λ < m and 0 < s < 1/(λ + m) are constants.
By applying the Nehari–Pohozaev manifold, we prove that our system has a
ground state solution.
We also prove that solutions of this system are radially symmetric and belong
to C0,μ(RN ) for some 0 < μ < 1 and each N > 1.
Description
Keywords
Pseudo-relativistic Schrödinger operator, Asymptotic linear system, Nehari–Pohozaev manifold
Citation
BUENO, H. P. et al. Results on a strongly coupled, asymptotically linear pseudo-relativistic Schrödinger system: ground state, radial symmetry and Hölder regularity. Nonlinear Analysis, v. 221, artigo 112916, abr. 2022. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0362546X22000839>. Acesso em: 06 jul. 2023.