In this example of man vs. self, Rainsford has been knocked out of his yacht and he is trying to reach land. In the first paragraph of page 3, the text says "He began to count his strokes; he could do possibly a hundred more..." This is an example of man vs. self because Rainsford has to convince himself that he can keep swimming, rather than giving up.
In this example of man vs. self, General Zaroff has just told Rainsford that he hunts people instead of animals. At the bottom of page 10 General Zaroff tells Rainsford, "we will hunt-you and I." This is an example of man vs. self because Rainsford must decide for himself if he will accept the general's challenge, face Ivan, rejecting the challenge, or find a way to escape "Ship-Trap Island."
In this example of man vs. self, Rainsford is hiding in a tree in the jungle, avoiding being caught by General Zaroff. On page 12 Rainsford says to himself "I will not lose my nerve. I will not." This is an example of man vs. self because Rainsford is all alone, telling himself to stay calm because he knows if he doesn't he won't be able to win the challenge and the general will kill him.