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 (lambda, mu) epsilon R-+(2) \ {(0, 0)}. We show that there exist three nonempty subsets of R-+(2) \ {(0, 0)}: Gamma, Delta(1) and Delta(2) such that R-+(2) \ {(0, 0)} = Gamma boolean OR Delta(1) boolean OR Delta(2) and the system has at least two positive periodic solutions for (lambda, mu) epsilon Delta(1), one positive periodic solution for (lambda, mu) epsilon Gamma and no positive periodic solutions for (lambda, mu) epsilon Delta(2). Meanwhile, we find two straight lines L-1 and L-2 such that Gamma lies between L-1 and L-2. (C) 2007 Elsevier Ltd. All rights reserved.