The reach of evil in The Lord of the Rings is wide, and spans across the whole of Middle-earth. Sauron's influence extended far beyond Mordor itself, and his corruption is seen in a number of characters that the Fellowship encounters over the course of their journey. Sauron wasn't stupid, and he knew that a good way to have power over the land was to infect those who were in positions of power with his evil ideals and have them work for him.
Of course, there were also just people that were corrupted by the foils of man, or by very human desires. Not everyone can blame their bad behavior on the Dark Lord's influence; sometimes they're just awful people to begin with, or at the very least, people who have become awful because of the choices they have made. Sometimes the line is a little more blurry, and it can be hard to tell which is which. Denethor is one such character where his true intentions and motivations are a little unclear. Was he just a terrible person to begin with, or was there some of Sauron's influence in the actions he took?
Who is Denethor?
Denethor II, son of Ecthelion II, was the Steward of Gondor. Stewards in Gondor were first the chief high counsellors to the Kings of Gondor, but they then became defacto rulers when those kings disappeared until Aragorn came back to claim his birthright as King. Denethor was the father of Boromir and Faramir, who both played important roles over the course of The Lord of the Rings. He was wise and insightful, and was very strong-willed.
Denethor had used a Palantír to see Sauron's strength, the effort of doing which aged him prematurely, and the knowledge of how vast and overwhelming the Dark Lord's forces were just made stronger the bitterness within him that had begun with the death of his wife years prior. Denethor knew that Sauron's attack on Gondor would happen within his lifetime, and he tried to prepare, even though deep down he believed the attempt to retaliate would be pointless. When Sauron attacked Osgiliath, he found that the strength of Denethor's army was more than he has planned for. The death of Boromir, his favorite son, sent him further into despair, as did the siege and imminent doom of Gondor. The films portray the character as an incompetent leader driven by impulse and insanity (brought on by that deep despair), but in the books he was a much more powerful leader, despite his eventual fall and the numerous flaws he possessed.
Was Denethor Corrupted By Sauron?
The answer to this is a little complex - it's both yes and no. The use of the Palantir that drove him to be upset in the first place was his own choice, and his despair came simply from seeing what he thought was the future. At this point, Sauron was not actually able to influence him in any way. The death of Boromir drove him closer to the edge, and he became estranged from his other son, Faramir. He dispatched Faramir to lead a charge at Osgiliath, but when Faramir returned with grave injuries, it just broke Denethor's spirit even more.
As he continued to look into the Palantír, Sauron was able to drive him mad by showing him a vision of an approaching fleet from the south that he believed to be Sauron's army. However, Sauron hid from Denethor that this fleet was actually commanded by Aragorn, who was showing up to save Gondor. Because of this, Denethor believed that it would be pointless to continue fighting against Sauron's forces. He then committed suicide by building a burning pyre for himself and Faramir (who he believed to be dying) and laying himself upon it, holding the Palantír the whole time. This is slightly different from the version in the Return of the King movie, where he is lit on fire and falls from the walls of Minas Tirith. Faramir was saved just in time and pulled off the pyre, but Denethor perished there and ended the Stewardship of Gondor.
So, in a way, Sauron did influence Denethor in the end, after showing him the vision. However, Sauron did not actually change Denethor's thoughts or heart in any way, he merely capitalized on the grief and despair that was already present. Denethor had started going down a dark path long before the end, mainly started by what he saw in the Palantír after his wife's death. Though he feared losing to Sauron, Sauron himself didn't have to do much to influence him and was never the initial cause of his actions. This makes Denethor one of the more interesting antagonistic characters in the series, as his thoughts and actions were his own, and were not totally being shaped by the will of the Dark Lord.