Existence and concentration of positive solutions for coupled Schrödinger equations

Abstract

In this paper, we study the existence and concentration of positive solution of a class of coupled Schrödinger equations. We admit that the potentials may not be non-negative and suppose that the intersection of the sets has positive Lebesgue measure. By studying the modified functional of the associated functional carefully, we establish the existence of positive least energy solutions for the coupled Schrödinger system. Moreover, we prove the concentration phenomenon of the positive solution when the parameter goes to infinity.

Keywords:

• Coupled Schrödinger equations
• positive solutions
• critical ponits

AMS Subject Classifications:

• 35J61
• 35J20
• 35Q55
• 49J40

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Natural Science Foundation of China [grant number 11201186], [grant number 11571140], [grant number 11371090]; Science Foundation of Jiangsu Province [grant number BK2012282], [grant number BK20150478]; Jiangsu University Foundation [grant number 11JDG117], [grant number 14JDG070].