Results on a strongly coupled, asymptotically linear pseudo-relativistic Schrödinger system : ground state, radial symmetry and Hölder regularity.

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.