Periodicity And Oscillation Of Solutions For Several Kinds Of Delay Differential Equations

This thesis of Master is composed of three chapters, which mainly study the periodicity and oscillation of solutions for several kinds of delay differential equa- tions.In chapter one,by means of the Krasnoselskii fixed-point theorem,we study the existence of positive periodic solutions for two kinds of neutral functional differential equations d/dt[X(t)-cx(t-T(t))]=-a(t)x(t)+t-f(t,x(t-T(t))),d/dt[x(t)-(?)Q(r)x(t+r)dr=-a(t)x(t)+b(t)(?)Q(r)f(t,x(t+r))dr, and some sufficient conditions are established. We improve some known result, and obtain some new result.Chapter two mainly considers the existence of positive periodic solutions for a neutral multi-delay logarithmic population model dN/dt=N(t)[r(t)-(?)aj(t)lnN(t-aj(t))-(?)bi(t)In N(t-r_i(t))]. We eliminate some Lemmas in relevant paper, by using an abstract continuation theorem for k-set contractive operator and some other analysis technique, establish some criteria to guarantee the existence of positive periodic solution.In the last chapter,we investigate the oscillation of first order nonlinear delay differential equations x′(t)+λx(t)+p(t)f(x(at))=0,x′+λx(t)+(?)pi(t)f(x(a_it))=0.We present infinite-integral conditions for the oscillation of equations, improve and generalize some known results.