Spectrum For The Periodic Eigenvalue Problems Of Second Order Half-Linear Differential Equation

We consider the half-linear peridie Sturm-Liouville problem-(py')'+qy=?ry+?y++?y-,y(a)=y(a+?) where y=[y,y']T,1/p,q,r,?,??L1[a,a+?]with 1/p>0. We will use the Prufer techniques to study eigevalue theory of right defmite(r>0),left definite (r>0,r<0)and right semi-definite(r?0)periodic eigenvalue problems. The main methods we use are a kind of Prufer transformation which are introduced by Binding and Volkmer[The Amer.Math.Monthly.2012].The main results in this thesis extend the corresponding results of Browne[Proc. Edinburgh Math. Soc., 1998],and improve and develop results of Binding and Volkmer[The Amer.Math. Monthly.,2012],Binding and Volkmer[J.Differential Equations,2013].