Positive Periodic Solutions For A New Class Of Delayed Differential Equations

One-order time-delayed differential equations has extremely importanttheory significance in the actual problem research and in particular,periodic solutions of equations can describe actual problem conditions precisely.There?fore,one-order time-delayed differential equations have been obtained massive discussions.In this paper,we discuss positive(^—periodic solutions for a new class of one-order time-delayed differential equationx~f(t)=—a{t)x{t)+Xb(t)F(t_^x(t—r(t))),where A is a positive parameter,a,6,r E C(R,R)are(^—periodic function with a,6>0,a,6^0,F E C(R x[0,oo),[0,??)).By using some recent new fixed point theorems in ordered Banach spaces,we give sufficient conditions to guarantee the existence of unique positive periodic solutions under increasing conditions and decreasing conditions.Finally,some simple example are given to illustrate the main results.