On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials

Mirko Tarulli and George Venkov ()
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Mirko Tarulli: Mathematics and Science Department, American University in Bulgaria, 1 Georgi Izmirliev Sq., 2700 Blagoevgrad, Bulgaria
George Venkov: Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, Bulgaria

Mathematics, 2023, vol. 12, issue 1, 1-21

Abstract: We present a generalized version of a Gagliardo–Nirenberg inequality characterized by radial symmetry and involving potentials exhibiting pure power polynomial behavior. 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 H s -subcritical nonlinearities, either of a local or nonlocal nature.

Keywords: fractional Laplacian; radially symmetric potential; nonhomogeneous potential; Gagliardo–Nirenberg inequality; nonlocal nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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