What was found
(CAN) THE CREW TRIED TO START APU 3 TIMES ON DESCENT. 1ST: NO RPM, AND LITTLE TO NO EGT. DID NOT START. 2ND: RMP WAS LOW AND EGT WAS ERRATIC. DID NOT START. 3RD: STARTED AND EGT SPIKED TO 640 AND CREW SMELLED BURNING ODOR. CREW SHUTDOWN APU AT THIS TIME. POST FLIGHT INSPECTION REVEALED HEAT DAMAGE AND SOOTING TO THE APU INLET AND JUST AFT OF THE INLET SCREEN. APU STARTER, INLET DUCT AND SCREEN TO BE REPLACED AND TAIL CONE TO BE REPAIRED.