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Bound and ground states of coupled 'NLS-KdV' equations with Hardy potential and critical power

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URI: https://hdl.handle.net/10016/39245
ISSN: 0022-0396
DOI: https://doi.org/10.1016/j.jde.2023.04.033
UXXI: AR/0000033749
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bound_JDE_2023.pdf (455.81 KB)
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2023-08-25
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Elsevier
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Abstract
We consider the existence of bound and ground states for a family of nonlinear elliptic systems in RN, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equa-tions are coupled by what we call "Schrodinger-Korteweg-de Vries" non-symmetric terms, which arise in some phenomena of fluid mechanics. By means of variational methods, ground states are derived for several ranges of the positive coupling parameter nu. Moreover, by using min-max arguments, we seek bound states under some energy assumptions.
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Doubly Critical Problems, Ground States, Hardy potential, Nonlinear Schrödinger systems, Variational methods, Bound states
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Burin, D., Kilteni, K., Rabuffetti, M., Slater, M., & Pia, L. (2019). Body ownership increases the interference between observed and executed movements. PLOS ONE, 14(1), Artículo e0209899. https://doi.org/10.1371/journal.pone.0209899
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