European feudal lords fought many wars in name of territorial claims originated through family ties. Let us assume the fictive Duke of X. He dies without and heir and two of his nephews – for the sake of the argument let us imagine that all of nephews were equally powerful Counts - lay claim to the duchy. If diplomacy fails to bring closure to such squabble, war would ensue. How would these nephews motivate peasants and minor nobility alike to fight for this particular claim? Where did the resources come from? How did one mobilize the manor for the war effort when this war is happening between cousins and has no sort of religious background that could serve as a motivator? Lastly, how frequent were these conflicts and how often did they escalate into an armed conflict?
Edit: My question was motivated after reading a bit on the Battle of Stamford Bridge in 1066 where Harald Hardrada, the King of Norway, fought Harold Godwinson for the English throne after the death of Edward the Confessor. Some of the sources I read stated that the Norwegians gathered an army of 9 thousand men and that made me wonder how one could keep such an army motivated to fight overseas if the reason behind the war was solely the King's personal claim to a title. Following on that reflection, I wondered if this sort of conflict was also common among the lower ranks of the feudal society such as wars for duchies. On that note, the geographic area I am interested of is medieval England and the period I am mostly reflecting upon is the XI century.
You're not going to get a good answer to this unless you specify exactly where geographically and narrow your time frame down significantly because depending on where and when you want to talk about, these things varied a great deal.
That said, in very general terms you don't have do motivate your subjects to fight for you, they are bound by law to do so and refusal was either punished by hefty fines or some other form (stipping of titles, forfeiture of land, prison etc). What the punishment was and how common refusal to fight was varied not only with geography and time period but also social strata. In some cases it might even have been acceptable to send someone to fight in your stead.
As to resources, I don't know if you're refering to monetary resources, equipment for soldiers or supplies for the troops in the field but again, this would have varied. In most early leavies the men subject to it were expected to supply their own arms and armor. This was the case in early medieval england and scandinavia for example. In other cases the lords armory would supply leavies with basic equipment. Money for payment (such as it is) would have come from the lords coffers although oftentimes leavies were not paid at all, the deed to their land was their payment, in return they pledged to fight when called upon or for a set number of days, weeks, months etc.
How did one mobilize the manor for the war effort when this war is happening between cousins and has no sort of religious background that could serve as a motivator?
I don't understand the question.
Lastly, how frequent were these conflicts and how often did they escalate into an armed conflict?
There is no way to quantify this without specifying time period and region but generally speaking one tried to avoid this kind of conflict whenever possible and rules of hereditary succession are generally constructed in such a way that two people never have identical claims to a title (through family trees, genealogies, ahnentafels etc). Also you're overlooking a principal function of the feudal system which is that almost everyone has a suzerain lord, that is to say, someone with a higher title to which you in turn have sworn fealty. That person is probably not interested in having you fight a civil war on a part of land that is part of his domain and may well simply step in and decide who gets the title. Again, depending on where and when, your suzerain overlord might even decide that you're both annoying and simply give the title to someone else.