Oscillation Of Solutions For Several Kinds Of Delay Equations

This thesis of Master is composed of three chapters,which mainly study the existence of positive solutions for several kinds of delay differential equations and oscillation of solutions for delay differential equations and delay difference equations.In chapter one,by using the fixed point theory,we study the existence of positive solutions for non-linear neutral delay differential equationsand linear neutral delay differential equationsChapter two firstly considers the oscillation of solutions for the first order linear delay differential equationWe improve some known result, and obtain a new oscillation result. We secondly study the following non-linear neutral delay differential equationsandSome sufficient conditions will be estabished for oscillation of every solution.In the last chapter ,we investigate equations d≥1One odd , k non-negative integer.α_i＞0, i＝1,2,…m And (?) = 1, {p(n)}, {q(n)}is a positive real series, and 0≤p(n)≤1,xf(x)＞0(x≠0),f∈C(R,R). f is monotonically increasing. By using some lemmas ,some sufficient conditions will be estabished for oscillation of every solution and its bounded non-oscillatory solutions asymptotic zero of the criterion is estabished,which improve and generalize some known results.