On eigenvalues of second order measure differential equation and minimization of measures.

In this paper, we consider eigenvalue problems of a second-order measure differential equation. We first study some general theories regarding the completely continuity of eigenvalues, the variational characterizations of eigenvalues, and the oscillating properties of eigenfunctions. Then, we solve the following minimization problem: when the m -th Neumann eigenvalue is given, to find explicitly what measures will have the minimal total variation. As applications of this minimization problem, we will solve some extremal problems of eigenvalues and construct some optimal classes of non-degenerate measures for the second-order measure differential equations. [ABSTRACT FROM AUTHOR]