While there are several theories to handle the conflict, but given my experience, I would like to call it a necessity and inevitable. Conflicts are necessary for mutual growth, brainstorming and thinking from a different perspective.
I have been so far successful in handling the conflicting situations effectively using 2FM method.
1) Find the source/objective of the conflict, whether it is valid and good for project or is there any other reason (personal, skill-gap or lack of information on either side).
2) Fix the reason. Try to bring the particular stakeholder to same level of understanding, request them to spend the time to develop the understanding about the project and then raise the conflict. Let them understand that negative conflict will only harm the project timelines and will result into business disruption.
3) Meet, collaboratively request parties to work on the resolution while not diluting your authority of being the project manager. Have some positive examples ready where conflicts help in overall development and growth. Show the leadership trait and induce the habit of being inclusive in parties who were in the situation of conflict.
It is a very effective method and works effectively if practiced thoughtfully. So this was how I was able to manage the conflicting situations easily and effectively.