- Both countries called for the peaceful resolution of the border dispute.
- Diplomats are hoping for a speedy resolution to the crisis.
- A resolution on Ukrainian independence was adopted by the Supreme Soviet.[FONT=verdana,geneva,lucida,'lucida grande',arial,helvetica,sans-serif]
[/FONT] There is no difference between 'of' and 'to' in my opinion. In your first two sentences, 'resolution' means 'solution, answer'.
In the third sentence, resolution means 'statement of opinion/decision/intent'. 'On' is correct, but 'about' is possible.