時標(biāo)上二階非線性動力方程的振動性和非振動解的分類與存在性.pdf

1、湘潭大學(xué)碩士學(xué)位論文時標(biāo)上二階非線性動力方程的振動性和非振動解的分類與存在性姓名：苗金鳳申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：周勇20060428AbstractTheory of time scales ,which was established on the basis of the theory of measurechains ,has received a lot of attention since Stafen Hi

2、lger[1] introduced it in his Ph.D.in1988.In this area,Bohner,A.Peterson,Agarwal etc. have done some important work.Butfew studies consider the oscillation of the second order nonlinear dynamical equationson time scales .

3、In this article ,we mainly discuss the oscillation and the existence of thenonoscillatory solutions of second-order nonlinear differential equation on time scales.Thearticle composes of four chapters .In chapter two ,we

4、give a introduction to the time scalesand introduce the preliminaries of dynamic equations on time scales.Chapter three andChapter four are the mainly results of this article,and we apply the behavior of stronglysuplinea

5、r and strongly sublinear of a function.In chapter three ,we get some sufficicentand necessary conditions for all the oscillatory solutions of second-order nonlinear dy-namical equation on time scales,and give proofs of t

6、hem.We get four theorems in thischapter ,namely we get sufficient and necessary conditions for all the oscillatory solu-tions of equation (r(t)x?(t))? + f(t, x(g1(t)), · · · , x(gm(t))) = 0 (E), ? ∞ t0 1r(

7、s)?s = ∞ or? ∞ t0 1r(s)?s < ∞ and f(t, x(g1(t)), · · ·, x(gm(t))) are strongly suplinear and strongly sublin-ear separately herein. Furthermore,our results unify and improve some known results ofneutral

8、 functional differential equations and delay difference equations in the references.In chapter four,with the references,we study the existence and asymptotic behavior ofthe nonoscillatory solutions of second-order nonlin

9、ear dynamical equation (E) on timescales,and give the classification according to their asymptotic behavior,namely,the classi-fication of all the nonoscillatory solutions of (E) when ? ∞ t0 1r(s)?s = ∞ and ? ∞ t0 1r(s)?s

10、 < ∞separately.Some sufficient and necessary conditions are obtained for all the solutions ofsecond-order nonlinear dynamical equation (E) to be nonoscillatory.Key words: Oscillation; Nonoscillation; Dynamical equatio