As you progress further in Pokemon Sun and near the end of the main storyline, you will have your chance at battling and capturing Solgaleo. Like many other Mascot Legendary Pokemon, Solgaleo makes for a very difficult capture. To start, odds are it will be equal or higher than most of the Pokemon on your team, sitting at a pretty decent level of 55. It will also probably be faster than most of your Pokemon, with a Base Stat of 97 (one of the higher Speed Stats in all of Alola). And let's not forget the offensive power and it has, plus its exclusive ability that prevents its stats from being lowered. Yeah, this thing won't be easy unless you're using a Masterball on it, which we don't recommend.
Here Are Some Tips For Catching Solgaleo:
Like most Legendary Pokemon that don't have the highest Level in-game, you should definitely only use Ultra Balls on Solgaleo, but only after getting its HP as low as possible. This can be incredibly difficult, since it won't have a problem crushing all sorts of holes in you team. And that's why you need to have more than the average amount of Ultra Balls, Revives and Hyper Potions.
False Swipe is also nice to have on one of your Pokemon, guaranteeing that Solgaleo will be left with at least one HP, should you have the TM or a Pokemon that knows it. Thunder Wave also works best as a status condition, since it's permanent (unlike sleep) and it doesn't cause Solgaleo to lose an HP.
And don't forget to ALWAYS save before facing Solgaleo. You are FORCED to capture Solgaleo, no ifs, ands, or buts about it. It's a safety precaution, one that has worked since the first generation of Pokemon.
I caught solgaleo with just 2 ultra balls xD . So I guess this wqs irrelevant for me. For the rest of you guys I guess it is relevant.