Abstract
This work studies the inhomogeneous Schrodinger coupled system
i(u)over dot(j) + Delta u(j) = -vertical bar x vertical bar(b) (Sigma(m)(k=1)a(jk)vertical bar u(k)vertical bar(p)) vertical bar u(j)&VERBAR(; p-2)u(j).
Using two criteria about scattering of global solutions and blow-up, one obtains some simplified proofs of the scattering versus finite or infinite time blow-up of energy solutions in three regimes: under, at and above the ground state threshold. This extends the previous work of the first author (Ghanmi and Saanouni, J. Math. Phys. 62, 101508 2021) to the non-radial settings. The ingredient used here are Strichartz inequalities, Morawetz estimates and a scattering criteria. The scattering proof follows the new approach due to Dodson and Murphy (Proc. Am. Math. Soc., 145(11) 4859-4867 2017). The main idea is that the decaying factor vertical bar x vertical bar(b), b < 0 in the source term obviates the need for a radial assumption.