Two Term Asymptotics Of Counting Function For One Dimensional P-Laplace Operator With Mixed And Periodic Boundary-value Conditions

In this paper, We study the spectral counting function for one dimensional p-Laplace operator. We prove the existence of a two term Weyl-type asymptotic with mixed and periodic boundary-value conditions. This is the generalization of Laplace operator with mixed and periodic boundary-value conditions.The thesis consists of three chapters. In Chapter 1, we introduce the background of the problem and give the main results of this paper. In Chapter 2, first we give some basic properties of the eigenvalues of the elliptic PDE operators, and then we introduce the definition of the Minkowski dimension, Minkowski measure and their properties, finally we introduce the definition and some basic properties of the generalized Sine-function and Riemann Zeta-function appearing in this paper. Our mainly results and their proofs are presented in Chaper 3. We get the exact second term of the spectral asymptotics formula.