Positive periodic solutions of second-order nonlinear differential systems with two parameters

By employing the Deimling fixed point index theory, we consider a class of second-order nonlinear differential systems with two parameters (@l,@m)@?R"+^2@?{(0,0)}. We show that there exist three nonempty subsets of R"+^2@?{(0,0)}: @C, @D"1 and @D"2 such that R"+^2@?{(0,0)}=@C@?@D"1@?@D"2 and the system has at least two positive periodic solutions for (@l,@m)@?@D"1, one positive periodic solution for (@l,@m)@?@C and no positive periodic solutions for (@l,@m)@?@D"2. Meanwhile, we find two straight lines L"1 and L"2 such that @C lies between L"1 and L"2.