I just bought a mobile charger(brandless, made in China).
It CAN charge my Samsung Galaxy S3, but CANNOT charge my Samsung Galaxy S4 and Note3(it will turn off automatically after a few seconds).
Why? How can I solve this problem? Or I really have to buy a new one to charge my S4 and Note3?
Please help me.

I have tried both 5V, 1A and 5V, 2.1A outputs
I have also tried the original cables.