Does Delaware tax all income for nonresident returns?

I lived in Pennsylvania while working in Delaware until August, and then moved to Illinois for a new job.

I am filing my DE nonresident return, and if I'm not mistaken Delaware wants to tax my earnings in Illinois, as well as my Delaware earnings.  I also had capital gains while living in Pennsylvania and Illinois, and Delaware wants to tax those earnings as well.  How does the Delaware non-resident return work?