Results on a strongly coupled, asymptotically linear pseudo-relativistic Schrödinger system: Ground state, radial symmetry and Hölder regularity. (August 2022) - Bueno, Hamilton; Mamani, Guido G.; Medeiros, Aldo H.S.; Pereira, Gilberto A.
Abstract: In this paper we consider the asymptotically linear, strongly coupled nonlinear system − Δ + m 2 u = u 2 + v 2 1 + s ( u 2 + v 2 ) u + λ v, − Δ + m 2 v = u 2 + v 2 1 + s ( u 2 + v 2 ) v + λ u, 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 C 0, μ ( R N ) for some 0 < μ < 1 and each N > 1 .