When a particular user creates a report, it is not appearing under his/her View / Run reports list, however the report has been successfully created and can be seen by an Admin.
UI14 or UI15
You may have accidentally clicked the star icon in the list header so only favorite reports appear. If some of your reports have not been marked as a favorite, then you would not be able to see or search for them.
Two simple solutions are:
In UI14, you can manually mark a report as a favorite by clicking the star icon beside the report title. To toggle between showing only favorite reports and showing all reports, click the star icon in the list header.
In UI14 on Fuji, a report is automatically marked as a favorite when you open the report.
Starting with UI15 (on Fuji and later), the new View/Run reports list layout uses the general Automatically Add Favorites per-user setting to define the preferred behavior. You can modify this by clicking the menu icon in the Application Navigator. Toggle the option to enable or disable automatically adding favorites (see below screen shot). The setting applies to the selection of both application menu modules and reports.