The ROSAT PSPC (Cat. <IX/11>) performed more than 200 pointed observations of the Large Magellanic Cloud (LMC) between 1990 and 1994. Most of the LMC was covered more than once and a large fraction at least ten times, making the PSPC observations an in valuable archive to study long-term time variability in the LMC. We performed a systematic search for variable X-ray sources in the LMC and found 27 sources which showed flux variations by factors between 3 and more than 1000. A comparison of the temporal and spectral characteristics of 15 X-ray sources which are not yet identified optically with those of the previously known sources in our sample allows to draw first conclusions about their nature. Up to six of the unidentified sources are promising candidates for high mass X-ray binaries in the LMC. Six sources are probably foreground stars, two soft objects might be supersoft sources and one source could be a black hole candidate. Most of the X-ray binary candidates are found in the area of the LMC 4 supergiant shell leading to a significant concentration of such systems in that region, consistent with the idea of being born in the stellar formation event which created the shell.