Oscillation And Existence Of Positive Solutions For Several Kinds Of Delay Differential Equations

In this thesis of master, we investigate the oscillatory and nonoscillatory behavior of the following first order linear and nonlinear delay differential equationsx′(t)+p(t)x(Î¥(t))=0, t≥t₀, (1.1.1)x′(t)+f(t,x(Î¥(t)))+h(t,x(t))=0, t≥t₀≥0, (1.1.2)in the critical state by using the oscillation criteria of ordinary differential equations. We also investigate the oscillatory and nonoscillatory behavior of the following first and odd order neutral delay differential equations with positive and negative coefficients[x(t)-R(t)x(t-r)]′+P(t)x(t-Î¥)-Q(t)x(t-σ)=0, t≥t₀, (2.1.1)[x(t)-R(t)x(t-r)]⁽ⁿ⁾+P(t)x(t-Î¥)-Q(t)x(t-σ)=0, t≥t₀. (2.2.1)We obtain many results on oscillation and nonoscillation of solution for the above equations. Some of them are new, some of them extend and improve the known results of many authors.