In Prisoner of Azkaban, Lupin says this:
“There are — certain defenses one can use,” said Lupin. “But there was only one Dementor on the train. The more there are, the more difficult it becomes to resist.”
In Half-Blood Prince, Harry thought this to himself:
Having wasted a lot of time worrying aloud about Apparition, Ron was now struggling to finish a viciously difficult essay for Snape that Harry and Hermione had already completed. Harry fully expected to receive low marks on his, because he had disagreed with Snape on the best way to tackle dementors, but he did not care: Slughorn’s memory was the most important thing to him now.
Both Lupin and Snape, with lots of experience in fighting against the Dark Arts, state that there's more than one way to fight a dementor, and Snape implies to Harry that the Patronus may not be the best one, as Harry only uses that to defend against dementors.
Also, Dementors are tangible, as it's actually the Dementors themselves who empty the cells of corpses and bury them in Azkaban's graveyard. Relatives of the dead prisoner are then free to visit the graves. That requires physical touch.
The Shield Charm can be used to repel physical objects and people, as Hermione showed when Harry and Ron had an argument in Winter of 1997, in the middle of the Horcrux Hunt. Does the Shield Charm and its variants work on Dementors?
