The power consumption of an e-ink ebook reader is quite low. An average user might need to charge it once a month. Even a very small solar panel should be able to generate enough power for it.
Are there any solar-powered ebook reader?
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Following this article, it looks like one has been developed by LG already:
Designed by LG Display, the sleek reader features a wafer-fin photovoltaic cell that provides it with a steady stream of solar energy.
Read more: LG Unveils Solar Powered E-Book Reader | Inhabitat - Sustainable Design Innovation, Eco Architecture, Green Building
EDIT: Found after digging some more through Google
Toshiba has decided to give their next gadget a green twist by announcing that their new eReader, the Biblio Leaf, will be solar powered
SolarFocus Technology Company Ltd. has just unveiled one of the most ingenious and practical solar powered gadgets that we’ve seen in a long time — a sun-powered cover for the most popular e-reader on the market, the Amazon Kindle.
It seems that there is one in development in Finland: Article.
A new Color e-Reader is being developed by five media companies based in Finland. Their intention is to offer a low cost device that can be charged via solar power and used primarily for the consumption of newspapers. There is a beta test beginning in November that will see the Helsingin Sanomat newspaper being delivered by their new cloud infrastructure.
One of the new things this reader has going for it is the solar cell battery. It will be able to recharge in direct or ambient light and this is currently the only way you can charge the device.
Here is the company website, but it doesn't seem to be very informative at the moment.
SolarMio provide integrated solar panels into their lighted cases for Kindle 4 and Kindle Touch devices. I bought 2 of their cases for the Kindle 4 in spring 2013 and they seem to be working well in Kenya where they're deployed with Kindles.
http://www.solarmio.com/en/4712389290366.aspx (Kindle Touch)
Thanks to the other answers for integrated e-readers.
BTW: One of the challenges with integrated devices discovered by worldreader http://www.worldreader.org is that people didn't want to leave them to charge in the sun. The risk of them 'disappearing' or being damaged was too great. However, apart from this challenge the SolarMio cases worked well in the field and seem both reliable and effective.