I cut the potatoes up. I boil them for 7 minutes and then I fry them 15 min in some olive oil, but they fall apart quickly.   When I remove the water from the boiling pan after 7 minutes, the potatoes are already almost falling apart.   I have tried to fry potatoes without bowling them for a while, but they still weren't done.   How do I get the potatoes not to fall apart and get at least a bit crispy?   
I think the clue here is that your potatoes are almost disintegrating after you've boiled them. If they're doing that, then they will only continue to disintegrate when you sauté or shallow fry them, which is what I assume you're doing and that will happen regardless of the type of potato you're using.  As others have rightly stated, some potato varieties are less inclined to 'disintegrate' than others, but moving to a waxy potato (firm) may stop the potato disintegrating but it may also not give you the texture you're trying to achieve - crisp on the outside and fluffy on the inside.   I my opinion you're better off sticking with a 'floury' variety of potato, but modifying your cooking technique to prevent disintegration. I'd suggest trying the following -   Experiment with boiling times. It sounds like you need to boil them for less time than you're doing, trying boiling for 5 minutes instead of 7. The potato should be part cooked, but not breaking up, because you'll finish the cooking in the hot oil. Strain your potatoes and immediately rinse them under cold water and set aside to dry. Put your frying pan on a low heat and let it heat up for a few minutes, pour in some olive oil and heat that for a few minutes more - it should not get too hot. Flick in a tiny droplet of water, it should just start to sizzle, if it immediately evaporates it's too hot.  You need to cook potatoes in olive oil on a low heat as olive oil can change properties if it's allowed to get too hot. But you also need to make sure the oil is hot enough, the potatoes should sizzle when added to the pan, if they don't it's not hot enough.  Practice on getting the temperature of the olive oil just right as this is important to the outcome of your sautéed potatoes. When the temperature is right, carefully tip your potatoes into the frying pan, separate them and let them fry for a good few minutes or so so they crisp on one side, now flick them over and let them cook on the other side. Keep doing this till they're done. Resist the temptation to bash them about and push them round the pan as this will cause them to fall apart.   They should not disintegrate but should crisp on all sides and be fluffy in the middle. 