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

publication date

  • August 2023

start page

  • 560

end page

  • 590


  • August


  • 365

International Standard Serial Number (ISSN)

  • 0022-0396

Electronic International Standard Serial Number (EISSN)

  • 1090-2732


  • 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.


  • Mathematics


  • bound states; doubly critical problems; ground states; hardy potential; nonlinear schrödinger systems; variational methods