Identification: ID/care help: Plant from China - white/yellow flowers, woody stalks

Could anyone help me to identify this plant? I bought it this weekend but feel it has quickly declined. Several leaves have turned black from the tip and crumbled inwards, although other leaves look great. The flowers also seem to fall of rather quickly. The man who sold it to me called this an "egg plant", but I have a feeling this common name was just made up, and even if not, Google searches keep turning up recipes! Thanks in advance.

 

Looks like Plumeria sp., Frangipani.