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arXiv · 2107.13899

Bound and ground states of coupled "NLS-KDV" equations with Hardy potential and critical power

Eduardo Colorado·Rafael López-Soriano·Alejandro Ortega
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Abstract

We consider the existence of bound and ground states for a family of nonlinear elliptic systems in $\mathbb{R}^N$, which involves equations with critical power nonlinearities and Hardy-type singular potentials. The equations are coupled by what we call ``Schr\"odinger-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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Eduardo Colorado, Rafael López-Soriano, Alejandro Ortega. 2021-07-29. Bound and ground states of coupled "NLS-KDV" equations with Hardy potential and critical power. https://arxiv.org/abs/2107.13899

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