In the permission schemes, you can give the "Edit" permission to the reporter alone. Just one thing to not though, reporter may not always be the person who creates it. You can create an issue based on another person, if you have the "Manage Reporter" permission.
Se https://confluence.atlassian.com/display/JIRA/Managing+Project+Permissions .
I guess you don't want to have only reporter able to edit an issue (the ones who solves the issues should also be able to edit). So one solution would be to give edit issue permission to Reporter and Assignee. All other Users will have browse projects to see all issues (and create issue permission in order to become reporter).
You would need to add assignable user permission and assign user permission to some people as well.
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