1) Give them their own state. This is difficult for quite many reasons, and Israel (by which I mean the current government) doesn't want that
2) Give them full citizenship rights equal to Israel's citizens, make sure they have a proper minority representation, and let them participate in the regular political processes. The current government certainly doesn't want that, and I have no idea what part of the Palestinians would want that.
3) Continue to treat them as sub-human, and deal with the consequences of the hatred that fosters. That seems to have been the "strategy" before October last year.
4) Try to exterminate or exile them, or at least decimating them to such an extend that the problem becomes smaller.
Since 1) and 2) are (again, from the perspective of Isreal's government) undesirable, and 3) has stopped working, 4) seems to be their current strategy.
Why is it Israel’s problem? There was a legal agreement in 1948. It could have been so simple.