he had to imposed a martial law on the border states. a martial law is a law administered by military forces that is invoked by a government during an emergency.
Delaware, Kentucky, Missouri, and Maryland
It applied to the Southern states (over which Lincoln had no authority) and not to the Northern slave states of Kentucky, Missouri and Maryland.
President Abraham Lincoln was worried about Maryland because it was a border state and he thought the state might succeed from the union. Kentucky, Missouri, and Delaware were also at risk because they were border states.
Skilful diplomacy by Lincoln in Kentucky and Missouri, along with some unlawful jailing of pro-Southern leaders in Maryland.
There were nine slave-states that did not immediately join the Confederacy; they were undecided. After Fort Sumter, four of them voted Confederate - Virginia, North Carolina, Tennessee, Arkansas. That left Kentucky, Missouri, Maryland, Delaware and District of Columbia. DC abolished slavery in the first few weeks. Delaware only sent a few regiments to the Confederacy, and was essentially loyal. Kentucky was in serious danger of seceding and Lincoln allowed it to stay neutral at the beginning for fear of upsetting powerful slave-owners. Maryland was in a similar position, but Lincoln reacted by (illegally) jailing pro-Confederate leaders. Missouri experienced sectional guerrilla warfare throughout the conflict, but did not actually secede.
Delaware, Maryland, Kentucky and Missouri. Maryland tried to join the Confederacy, but Lincoln had the governor and the legislators arrested and put in prison without trial, and suspended the writ of habeus corpus to get away with it, to keep them from seceding. The Maryland leaders were replaced with pro-Union men. After seeing what happened to Maryland, Delaware did not try. Maryland sent soldiers and units to both sides, though, and so did Kentucky and Missouri.
...didn't want to upset the four slave-states which had remained loyal - Kentucky, Missouri, Maryland, Delaware.
Because he was keen not to upset the people of Kentucky, Missouri, Maryland and Delaware - slave states that had stayed loyal.
Because it allowed slavery to continue in the four slave-states that had stayed loyal (Kentucky, Missouri, Maryland, Delaware).
They didn't. Missouri suffered guerrilla war throughout the conflict, but did not secede. Kentucky was allowed to remain neutral at the beginning, and then voted against secession. An alternative Confederate government was set up there when Bragg invaded, but it collapsed when he retreated. Maryland probably would have seceded, had not Lincoln (illegally) jailed its pro-Confederate leaders.
The Buffer States - Kentucky, Missouri, Maryland, Delaware. Lincoln's chief priority at the outbreak of the war was to keep these four states in the Union.
There were four: Kentucky, Missouri, Maryland and Delaware. (And the Western counties of Virginia, which soon formed their own non-Confederate state, West Virginia). Lincoln was especially anxious not to upset the people of these states and drive them into the arms of the Confederacy. When he issued the Emancipation Proclamation, he allowed these 'Buffer States' to continue practising slavery until the war's end.