Limits Of One-dimensional P-laplacian Eigenvalues When The Interval Shrinks To An End Point

In this paper, Limits of p-Laplacian eigenvalues when the interval shrinks to anend point under separated boundary conditions will be considered.The paper is mainly divided into four chapters.The first chapter is the introduction of the whole paper. We talk about the back-ground of this problem, and make plans for the research of the problems.In the second chapter, We give some definitions and basic conclusions, such asp-Laplacian, Pru¨fer transformation and the properties of Pru¨fer angle, a generalizationof the familiar trigonometric functions and their properties.The third chapter is the main part of this paper, consisting of two sections. Thefirst section makes a Pru¨fer transformation for the one-dimensional p-Laplacianand we discuss the properties of corresponding Pru¨fer angle. In the second section, usingthe Pru¨fer angle and its properties discussed in the first section, we discuss the limitsof eigenvalues when the interval shrinks to an end point under separated boundaryconditions. It is shown that all the eigenvalues except the first approach+∞. Theseparated BCs for which the first eigenvalues λ0always tends to+∞or to+∞aregiven, and we make a discuss for the remaining situations.At last, we summarize the results of the whole paper.