Conflict is defined as a struggle or clash between two entities in a story, typically between the story's protagonist and antagonist. Since conflict refers to a struggle between two things, we can easily identify a specific conflict in a story as something vs. something else. Conflicts can be both external and internal. Common external conflicts are character vs. character, character vs. society, and character vs. nature. An internal conflict is commonly described as character vs. self. Many different conflicts, both external and internal, can certainly be found in Antoine de Saint-Exupery's novella The Little Prince.
One conflict can be seen with respect to the reasons behind the Little Prince's decision to leave his planet. On his planet, he met and started tending a rose he loved very dearly. Yet, due to her vanity and pride, he felt that nothing he could do for her was good enough; he felt that she did not love him as he loved her and made up his mind to leave though it broke his heart to do so. However, before he left, she confessed her love for him and begged his forgiveness. Since it was the flower's vanity that drove him from his own planet, we can call this conflict character vs. character.
Through his travels, the Little Prince experiences personal growth. As part of his personal growth, he battles with his feelings for his flower. At one point, he sees a garden of roses, and his prior belief that his flower was "unique in all the world" is temporarily shattered. It is the fox that convinces him his flower is unique in comparison to all other roses simply by virtue of the fact that he loved her. As he continues his journey, he upbraids himself for having left. All of these conflicting and changing emotions within the prince are examples of an internal conflict that we can call character vs. self.
Even the pilot struggles with his own inner desires and thoughts as he struggles to survive in nature and escape death; all of these struggles are also examples of both internal and external conflicts.