Want people to actively participate in your meetings? You may have to provoke them a bit. The following are some good ways to get the team involved.
Bring a tennis ball or some other kind of soft ball and gently throw it at the person you are asking a question, or at the person who just spoke up. Other props like that can make for a dynamic meeting environment and can be fun at the same time.
Instead of using the generic statement "So, who has an idea of what we can do about this?" ask someone by name, like "Ben, do you have any thoughts on this topic?" for example.
People typically think in terms of their own areas of expertise and responsibility and may not be aware that they can or should provide input unless prompted to do so. You can appeal to their expertise when eliciting their opinion by saying "Mark, help us think this through from a design perspective?" or "Jen, do you have anything to add? Maybe there...