What are some ways to know if my boyfriend is satisfied sexually?

Ask him. If you really don't know, then you may already be having a problem. Or you could be just be insecure. Talk to him, with your clothes on in a non stressful environment. If you initiate sex at least once in a while and if you change what you do now and then he should be satisfied. If every sexual contact is the same and he always has to ask for sex he may be wanting a change.