Have you tried thinning the fruit out at an early stage? Extra feed & watering might help too. You haven't said where you are so I don't know your weather conditions. Also do you know what type of pear it is? Most pears are not self-fertile so you need another, nearby tree of a different type which flowers at the same time for pollination

Knowing the variety of pear and at least what country you're in would be useful. If you're in the UK, then the drought conditions this year could explain why the fruit did not continue to develop (though knowing which bit of the UK you're in would help with knowing if that could be a possible cause), but if you could post a photo, that would also be helpful. Your general location is actually quite important...

Otherwise, is there any problem on the tree itself - on the branches, foliage and especially the underside of the leaves?

I used to have a wonderful d'Anjou pear tree (thank you hurricane Sandy). d'Anjou pears are gnarly looking things, but one of the best tasting pears you can get. I miss that tree.