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

Author

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  • Mirko Tarulli

    (Mathematics and Science Department, American University in Bulgaria, 1 Georgi Izmirliev Sq., 2700 Blagoevgrad, Bulgaria
    Institute of Mathematics and Informatics, Bulgarian Academy of Science, Acad. Georgi Bonchev Str., Block 8, 1113 Sofia, Bulgaria
    Department of Mathematics, University of Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy
    These authors contributed equally to this work.)

  • George Venkov

    (Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1756 Sofia, Bulgaria
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Mirko Tarulli & George Venkov, 2023. "On a Generalized Gagliardo–Nirenberg Inequality with Radial Symmetry and Decaying Potentials," Mathematics, MDPI, vol. 12(1), pages 1-21, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:8-:d:1303337
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    References listed on IDEAS

    as
    1. Van Duong Dinh, 2021. "Global dynamics for a class of inhomogeneous nonlinear Schrödinger equations with potential," Mathematische Nachrichten, Wiley Blackwell, vol. 294(4), pages 672-716, April.
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