- Advances in Nonlinear Analysis Journal
- November 2017
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- We show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger-Korteweg-de Vries equations. More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient satisfies beta >Lambda (for an appropriate constant Lambda > 0) or if beta > 0 under appropriate conditions on the other parameters of the problem. We also prove that there exists a positive radially symmetric bound state if either 0 < beta is sufficiently small or if 0 < beta < Lambda under some appropriate conditions on the parameters. These results give a classification of positive solutions as well as the multiplicity of positive solutions. Furthermore, we study systems with more general power nonlinearities and systems with more than two nonlinear Schrödinger-Korteweg-de Vries equations. Our variational approach (working on the full energy functional without the L2-mass constraint) improves many previously known results and also allows us to show new results for some range of parameters not considered in the past.
- variational methods; ground states; bound states; critical point theory; perturbation methods