Sharing links is great, but they take people away from your page. You need to engage your fans in a way that will encourage them to not only stay on your page, but have an opinion about your post and either like it or comment on it. One way to do this is to ask questions. But you have to ask the right kinds of questions.
I found a list of 16 different kinds of questions you can ask, from a blog by John Hayden: http://www.johnhayden.com/. Below I've listed my favorites.
1. Ask specific questions: Don't ask open-ended questions that require long answers; your fans will skip right over that post. They don't want to do homework, so make it as simple and specific as possible.
2. Ask true or false/yes or no questions: Again, if a simple answer is all that is required, your fans will more likely answer.
3. Ask poll questions: The "Questions" feature on Facebook allows you to create a poll. This one is fun; you can see which way the poll leans as more people answer. Plus, all your fans have to do is click on their preference; no need to even type an answer.
4. Ask directly: Especially if your Facebook page is new and you don't have much activity yet, ask specific fans you know personally to make a comment on your post. If you tell them you would like their input and think it would add value to your page, they'll probabaly be more than happy to post something.
5. Ask fun questions: You CAN go off topic with you fans. It will remind them that you are a person too, and it will help create more of a human connection with them.
Different types of quesitons are going to work better for some companies than others. Just keep in mind who your fans are (your target audience), and what motivates them to interact with you. Also, don't forget to pay attention when people answer your questions, and make sure to acknowledge them. Comment back and keep the conversation going.
Try some of these out and let me know how they worked for you!