Multiple Solutions To First-order Singular And Nonsingular Periodic Systems

In the first part, this paper is devoted to establish the multiplicity of positive solutions to first order singular periodic systems(1．2) where f(t,x,y)(i = 1,2) may be singular at (x,y) = (0,0) , the results may extend to more general form of f. It is proved that such a problem has at least two positive solutions under our reasonable conditions. The existence of the first solution is obtained by using a nonlinear alternative of Leray-Schauder, and the second one is found by using a Krasnoselskii fixed point theorem in cones.In the second part, this paper is devoted to establish the multiplicity of nonnegative solutions to first order nonsingular periodic systems(1．3) (1．4) The existence of solutions is obtained by using a Krasnoselskii fixed point theorem in cones.