Oscillation For Delay Dynamic Equations On Time Scales And Existence Of Positive Solutions For Partial Difference Equations

This thesis is composed of two parts.The first part is the introduction. On one hand, the backgrounds of this subject and development of studies are summarized simply. On the other hand, the main results of this thesis is introduced briefly.The second part is the main body of the article. It is composed of two chapters, which respectively study oscillation solutions of a class of nonlinear delay dynamic equations on time scales and the existence of unbounded positive solutions of certain delay partial difference equations .In Chapter two, the author establishs the equivalence of the oscillation of second order nonlinear delay dynamic equationsand second order nonlinear dynamic equationsxA(t)+p(t)(fox)=0on time scales, from which the author obtains some new oscillation criteria and a comparison theorem for the first equations. The author also obtains some new oscillation criteria for second order linear dynamic equations on time scales.In Chaper three, the author considers higher order nonlinear neutral partial difference equations of the formAA(o;OT>n - cxm_k,n-l) + f(m,n,xAnd obtains some sufficient conditions for the existence of unbounded positive solutions of this equation for c R using a fixed point theorem.