Is there any requirement to cite recent literature in publications?
This question seems to be based on a common misconception about the role of citations (see this question for a related issue).  Citations aren't just there to list content your work builds on; they're also there to provide the reader with context and motivation.

The reason you should be citing recent work is to help the reader.  If you were familiar with various unsuccessful solutions, it's likely that some of them motivated the successful one, even if only by identifying things that couldn't work, and that merits a citation.  Even if not, many of your readers are likely to be people who've thought a lot about one or more of those unsuccessful approaches; you're in the best position to explain how your approach differs.

(I'm writing from the perspective of mathematics, by the way.)