EU citizens have the right to work, study or reside in Sweden without applying for a residence permit. The right for EU members to stay in Sweden without a residence permit is called the right of residence. The right of residence applies to employees, self employed persons, students or those who have sufficient funds to support themselves in Sweden. If you are a citizen of a EU or EEA country and are planning to live in Sweden for one year or more, you are generally required to be registered in the Swedish Population Register.
Please visit the Swedish Migration Agency's website for more information: Work, study or live in Sweden for EU citizens, Nordic citizens and family members of EU citizens – Swedish Migration Agency