Positive Periodic Solutions of Systems of First Order Ordinary Differential Equations
نویسندگان
چکیده
Consider the n-dimensional nonautonomous system x(t) = A(t)G(x(t)) B(t)F(x(t r(t))) Let ( ) J, 1. EM I i 1. EM . 1 F (j ' j n ) F U U"...,Un, a lmllull-a lIull' 00 Imllull-oo lIull' Z ,...,n, ,..., , amaxi=l,...,nUJ} and Foo = maxi=l,...,n{f~}. Under some quite general conditions, we prove that either Fa = 0 and F 00 = 00, or Fa = 00 and F 00 = 0, guarantee the existence of positive periodic solutions for the system for all A > O. Furthermore, we show t,hat Fa = F 00 = 0, or Fa = F 00 = 00 guarantee the multiplicity of positive periodic solutions for the system for sufficiently large, or small A, respectively. We also establish the nonexistence of the system when either Fa and F 00 > 0, or Fa and F 00 < 00 for sufficiently large, or small A, respectively. We shall use fixed point theorems in a cone.
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