Although "Leiningen Versus the Ants" contains a strong external conflict -- Man vs. Nature -- it has little obvious internal conflict; from the beginning of the story, Leiningen is determined to fight the ants, and the events that follow show his will to continue. Leiningen does not vary from his original purpose, but does exhibit a moment of self-doubt as the ants threaten to overcome his defense:
...he felt for the first time since the arrival of the ants that his confidence was deserting him. His skin began to creep; he loosened his collar. Once the devils were over the trench there wasn't a chance in hell for him and his men. God, what a prospect, to be eaten alive like that!
(Stephenson, "Leiningen Versus the Ants," classicshorts.com)
The fear of being eaten alive by the ants gives Leiningen his internal conflict; is it worth continuing to fight, knowing that he might lose and be consumed in such a horrible fashion? However, as he fights the ants, Leiningen comes to the conclusion that he will not give up and run, but will fight until his last breath; he feels that he owes that to both his men, who believe in him and fight for him, and for his own personal pride. In this manner, he resolves his internal conflict.