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Hi there Malin,
You can use our "Unique Question" feature. Once you set your form's email field as a unique question, multiple submission using the same email address will not be allowed.
Here is a guide which should help you: http://www.jotform.com/help/223-How-to-set-Form-Limits-Based-on-a-Unique-Question
If you need further assistance please feel free to ask. Have a nice day.