Navegando por Autor "Mamani, Guido Gutierrez"
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Item Ground state of a magnetic nonlinear Choquard equation.(2019) Bueno, Hamilton Prado; Mamani, Guido Gutierrez; Pereira, Gilberto de AssisWe consider the stationary magnetic nonlinear Choquard equation −(∇ + iA(x))2u + V(x)u = (1|x|α ∗ (|u|) ) f(|u|) |u| u, where A : RN → RN is a vector potential, V is a scalar potential, f : R → R and F is the primitive of f . Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik–Schnirelmann methods.Item Results on a strongly coupled, asymptotically linear pseudo-relativistic Schrödinger system : ground state, radial symmetry and Hölder regularity.(2022) Bueno, Hamilton Prado; Mamani, Guido Gutierrez; Medeiros, Aldo Henrique de Souza; Pereira, Gilberto de AssisIn 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.