To keep, means to hold on to something, or not to let something go, to protect it. Examples... You keep your money in your wallet; you keep your ice cream in the freezer; you keep your clothes in the closet; you keep your car in the garage; they keep their son out of school, etc. (keep + noun/pronoun). (Keep on + verb) "Keep on" is used with a verb and implies that an action is going to be continued. Examples... He is going to keep on going to school. She kept on running after she stumbled. He kept on laughing when everyone else stopped. Keep on smiling in spite of difficulties. Give up & give up on, are more closely related, and I am finding it hard to explain the differences... Here is a website that will give you some help, and some examples... http://www.usingenglish.com/reference/phrasal-verbs/give+up.html http://www.usingenglish.com/reference/phrasal-verbs/give+up+on.html