A research problem is an area of concern or a gap in the existing knowledge that points to the need for further understanding and investigation. A problem statement is used in research work as a claim that outlines the problem addressed by a study. The problem statement briefly explains the problem that the research will address. 

Here are a couple of articles that will tell you how exactly you can write a great problem statement for your research:

• The basics of writing a statement of the problem for your research proposal
• Can you help me write a problem statement for my thesis?