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On a Generalized Gagliardo-Nirenberg Inequality with Radial Symmetry and Decaying Potentials
Version 1
: Received: 4 November 2023 / Approved: 6 November 2023 / Online: 6 November 2023 (13:40:12 CET)
A peer-reviewed article of this Preprint also exists.
Tarulli, M.; Venkov, G. On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials. Mathematics 2024, 12, 8. Tarulli, M.; Venkov, G. On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials. Mathematics 2024, 12, 8.
Abstract
We establish a new Gagliardo-Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behaviour. As an application of our result, we investigate the existence of extremals for this inequality, which also correspond to stationary solutions for the nonlinear Schrödinger equation with inhomogeneous nonlinearity, competing with Hs-subcritical nonlinearities, either of local or non-local nature.
Keywords
Fractional Laplacian; radially symmetric potential; non-homogeneous potential; Gagliardo-Nirenberg inequality; non-local noninearity
Subject
Computer Science and Mathematics, Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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