Monotonicity And Uniqueness Of Positive Solutions Of Degenerate P-Laplace Equations

In this paper, we use the sliding method to prove monotonicity in one direction and uniqueness of degenerate p-laplace equations in a bounded domain. First, we prove the regularities of the weak solutions of the equations and use the regularities to get a weak comparison theory. Then use the weak comparison theory and the sliding method, we prove the monotonicity and uniqueness of the positive solutions of degenerate p-Laplace equations in a bounded and smooth domain.