I don't know where you are, but in you're South of Watford in the UK, probably heat stress from the heatwave we had a couple of weeks ago - these plants do not like a lot of heat and a full sun position would have meant it got a lot.

Can't say much, nor tell you what can be done without more info, like is it in the ground or in a pot, and is it a standard (straight stem with the plant growing on top) or a bush. You can add this info by clicking in the box below this answer and typing it there. Or add a photograph, up to you.

We live in southern Ontario, Canada. We have not had a lot of rain in the past month but I've been watering faithfully, but maybe not enough? Everything else in the garden is ok. And only one half of the plant is affected. It is a bush, in the ground, about 4ft high and 5 or 6ft wide. We are currently in a bit of a heatwave, with temps in the high 20's and 30'sC. I am trying to just leave it alone, hoping it will renew itself. I am puzzled as to why only half the bush is affected. Thanks for any help/suggestions you can give me. I will take a pic today and forward.

I'm very interested to know whether the part that's dying back is all coming from one main branch at the bottom, where it comes out of the ground, or whether the die back is on various branches with different points of origin from the ground, if you can check that please. A photo of the plant would be very useful too, the whole plant, that is.

Here we are two years later and I am happy to say that my dappled willow is doing just beautifully. The offending part was cut off entirely, it appeared to be a separate graft and looked like some rabbits had been nibbling on it which probably caused its demise. It has adjusted and this year has grown significantly, looking full and varigated. We do, however, have to watch out for wild rabbits around here as they love to eat the shrubs especially during the winter months. Everything is covered with burlap and chicken wire! Also in the summertime with the willow I wrap foil around the main trunks to deter the little varmints and it seems to be working. These trees take a lot of water I have found, if we don't get rain for a week or so the tips start to turn brown but it quickly recovers once it gets a good soaking. A lot of work this species is but worth it. It's a show stopper in the garden. I will upload a picture. A belated thanks for your input!