On coupled systems of nonlinear Schrödinger equations with critical exponential growth

Abstract

In this paper, we prove the existence of positive ground state solutions to the following class of coupled systems involving nonlinear Schrödinger equations

where the nonlinearities and have exponential critical growth of the Trudinger–Moser type. Moreover, the coupling term satisfies . We use the minimization technique over the Nehari manifold and strong maximum principle to get a positive ground state solution.

Keywords:

• Critical growth
• coupled systems
• lack of compactness
• ground state

AMS Subject Classifications:

• 35J50
• 35B33
• 35Q55

Acknowledgements

The authors would like to express their sincere gratitude to the referee for carefully reading the manuscript and valuable comments and suggestions.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The research was partially supported by CNPq; CAPES/Brazil.