On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials-Reference-Cited by-同舟云学术

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

Published:2023-12-19 Issue:1 Volume:12 Page:8
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Tarulli Mirko¹²³^ORCID,Venkov George⁴^ORCID

Affiliation:

1. Mathematics and Science Department, American University in Bulgaria, 1 Georgi Izmirliev Sq., 2700 Blagoevgrad, Bulgaria

2. Institute of Mathematics and Informatics, Bulgarian Academy of Science, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, Bulgaria

3. Department of Mathematics, University of Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy

4. Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, Bulgaria

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 Hs-subcritical nonlinearities, either of a local or nonlocal nature.

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/12/1/8/pdf

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