E-resources
Peer reviewed
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Campos, Luccas; Guzmán, Carlos M.
Calculus of variations and partial differential equations, 08/2022, Volume: 61, Issue: 4Journal Article
We consider the focusing inhomogeneous biharmonic nonlinear Schrödinger equation in H 2 ( R N ) , i u t + Δ 2 u - | x | - b | u | α u = 0 , when b > 0 and N ≥ 5 . We first obtain a small data global result in H 2 , which, in the five-dimensional case, improves a previous result from Pastor and the second author. In the sequel, we show the main result, scattering below the mass-energy threshold in the intercritical case, that is, 8 - 2 b N < α < 8 - 2 b N - 4 , without assuming radiality of the initial data. The proof combines the decay of the nonlinearity with Virial-Morawetz-type estimates to avoid the radial assumption, allowing for a much simpler proof than the Kenig-Merle roadmap.
