Who cares if Hamas is popular ? The Nazis were pretty popular in Germany some decades ago.
My solution:
Israel steps up its liquidation process of terrorist leaders, while continuing to finish building the wall, inorder to keep out genocidal undesirables. There should be strikes every single day.
Kill Arafat. Get it over with. There will be a bunch of angry people, dancing in the streets, screaming for revenge. Pretty much the way the situation is today, whenever some lowlife terrorist bites the dust . Arafat is as helpful to the palestinians as Jim Jones was helpful to his followers. He is also taking them down the same path. Even with various prime ministers, Arafat is still the man in charge, as evidenced by the fiasco with the previous prime minister, abu mazan. So, quite simply, get rid of Arafat.
After the wall is finished, genocide bombers will find it harder to sneak into Israel, and the palestinians living behind the wall will have two choices.
(1) Get their act together, inorder to improve their situation.
(2) Continue with their current act and support for terrorists, which in turn will lead to a worse situation for them. Let them rot behind the wall, if they choose option #2.
Allow an international force to enter the palestinian areas, to keep peace/order, since the palestinians do not wish to keep peace or deal with criminals among them. Also, implement sterilization techniques and-or birth quotas for that impoverished society.
After a time of rotting behind the wall, in their selfmade poverty, perhaps some palestinians will want to seek out the peace option, instead of the terror option.
There wont be any peace as long as the majority supports murderous groups such as hamas, etc. Anybody who is a member of hamas should not feel safe. A re-education of that whole, violent society is in order, if they are to change their barbaric ways.
Also, I see all out war as a viable option, as this would solve the problem, and that is what the majority of palestinians want anyhow, which is evidenced by their massive support for terror groups.
Israel has flourished for decades, despite thousands of attacks and countless wars. Meanwhile the situation for the palestinians has gotten worse and worse, and will continue to do so, unless they get some non violent peace movements started.