AFTER A 2 PT 5 FUEL BURNOFF AND FLY-BY; A CPR JET CREW RETURN LAND AFTER CREW HAD DISCOVERED THAT THE NOSE LNDG GEAR CANNOT FULLY RETRACT OR EXTEND FROM ITS JAMMED POS AFTER TKOF FROM ZZZ.

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DEPARTING ZZZ RWY 17 AFTER CLRED FOR TKOF; STANDARD CALLOUTS WERE MADE. V1/V2; TKOF WAS INITIATED BY CAPT; GEAR UP; V2 +1 KTS FLAPS UP. WHEN GEAR WAS BROUGHT UP BY CAPT; THE NORMAL QUIETNESS THAT FOLLOWS WAS NOT PRESENT. WE PROCEEDED ON A CLBING R TURN; CLBING TO 5000 FT. WE PROCEEDED ON 'AFTER TKOF' CHKLIST. WHEN WE GOT TO 'GEAR' ON CHKLIST; WE BOTH (CAPT AND I) NOTICED 'GEAR UNLOCK' ABOVE THE GEAR LIGHTS. CAPT SLOWED ACFT FROM ACCELERATION (170 KTS). ATC WAS NOTIFIED OF LEVELOFF AND ATC WAS VERY COMPLIANT TO SIT. THE GEAR WAS CYCLED TO 'GEAR DOWN.' WE GOT THE L AND R MAIN GEAR GREEN LIGHTS AND STILL A 'GEAR UNLOCKED' LIGHT. NO NOSE GEAR LIGHT. CHKLIST WAS USED TO EXTENT OF EMER. EACH ITEM WAS CAREFULLY READ AND THEN COMPLIED WITH. NOSE GEAR STILL DID NOT EXTEND. WITH 5000 LBS OF FUEL; IT WAS DETERMINED TO STAY AT 2000 FT. APCH FLAPS LOWERED AND BURN OFF FUEL. (WE HAD APPROX 2+ HRS TO BRAINSTORM FURTHER.) ATC GAVE US FULL COMPLIANCE. (WE DID A FLY-BY DOWN RWY 1 AT ZZZ.) THE TWR CONFIRMED '2 MAIN GEAR DOWN;' APPEARED LOCKED AND NOSE GEAR DOORS OPEN AND NOSE GEAR TIRE WAS JUST VISIBLE. WE EXITED THE AREA AND LOITERED NW; THEN S OF THE ARPT. VIA RADIO FREQ TO FBO; OUR CHIEF PLT WAS NOTIFIED. HE CONTACTED FBO. THEN FBO WITH WICHITA WAS NOTIFIED. WE HAD DONE EVERYTHING THEY SUGGESTED UP TO THAT TIME. WE ASKED FBO WHETHER THEY THOUGHT ABOUT A FIRM TOUCH-AND-GO MIGHT BRING THE NOSE GEAR DOW. IT WAS THOUGHT BY ALL; US THE CREW; AND WICHITA; THAT IT WOULD AND SHOULD BE TRIED. WE MADE A TOUCH-AND-G0 ON RWY 17 AT ZZZ. WICHITA SUGGESTED VREF +20 KTS AND APCH FLAPS. THIS WAS PERFORMED. WE TOUCHED DOWN; CLBED BACK UP; ASKED THE TWR FOR A VISUAL. THEY STATED THE SAME 'MAIN GEAR DOWN; NOSE GEAR DOORS OPEN; NO NOSE GEAR!' DURING THE ENTIRE FLT; THE PAX WERE BRIEFED MULTIPLE TIMES; BY COPLT; FOR EXPLANATION OF WHAT HAPPENED; WHAT WAS BEING DONE BY THE CREWS. COPLT BRIEFED ALL PAX OF EMER EXITS AND CABIN MAIN DOOR. THIS COM WITH THE PAX; I BELIEVED; WAS VERY GOOD FOR PAX REASSURANCE. THEY; FOR THE MOST PART; REMAINED VERY CALM. WHEN FUEL WAS BURNED OFF TO APPROX 1200 LBS; OUR FINAL APCH TO LNDG WAS MADE TO RWY 13 (BECAUSE OF EXTRA LENGTH OF RWY AND SHIRTING WIND). EMER CREWS WERE IN PLACE. ALL INFO; SOULS ON BOARD; PLTS' NAMES; ETC; WAS GIVEN TO ATC. ALL LNDG CHKS WERE MADE AND SPDS FOR LNDG RECOMPUTED. CAPT TOUCHED DOWN SMOOTHLY (FULL FLAPS WERE USED). CAPT ACTIVATED THRUST REVERSERS. COPLT CALLED '6 LIGHTS;' CAPT USED REVERSERS. NOSE REMAINED WELL OFF. SPD BRAKES (WING) WERE USED. CAPT HELD THE NOSE OFF. NOSE REMAINED UP; SPD SLOWLY BLED OFF AND NOSE SLOWLY TOUCHED DOWN. ACFT SLID TO A VERY SMOOTH STOP. COPLT ACTIVATED FIREWALL SHUTOFF VALVES. COPLT TOLD PAX TO PREPARE FOR EXIT. I OPENED THE DOOR WITHOUT EFFORT. I HELD DOOR DOWN TO PAVEMENT WITH MY FOOT. ALL PAX EXITED ACFT AND EXITED OFF RWY 13. CAPT SECURED ACFT WITHOUT PAUSE AND WE BOTH (CAPT AND COPLT) EXITED ACFT AND WALKED AWAY FROM ACFT. CAUSE OF NOSE GEAR MALFUNCTION HAS YET TO BE DETERMINED. ACFT RECEIVED VERY MINOR DAMAGE TO NOSE. NO BUCKLING; ETC; WAS OBSERVED.