Minimization of eigenvalues and construction of non-degenerate potentials for the one-dimensional p-Laplacian.

We first use the Schwarz rearrangement to solve a minimization problem on eigenvalues of the one-dimensional p-Laplacian with integrable potentials. Then we construct an optimal class of non-degenerate potentials for the one-dimensional p-Laplacian with the Dirichlet boundary condition. Such a class of non-degenerate potentials is a generalization of many known classes of non-degenerate potentials and will be useful in many problems of nonlinear differential equations. [ABSTRACT FROM AUTHOR]