A Note on a Damped Focusing Inhomogeneous Choquard Equation

This paper is devoted to the focusing inhomogeneous Choquard equation with linear damping: i(u)over dot + Delta u + iau = -vertical bar x vertical bar(-gamma)(I-alpha*vertical bar u vertical bar p)vertical bar u vertical bar(p-2)u on R-N, where a >= 0 and 0 < gamma < inf(N, 2 + alpha). Global existence and scattering are proved for sufficiently large damping. For arbitrary damping, global existence of solutions is obtained if the initial data belong to some invariant sets.