Positive periodic solutions for multiparameter nonlinear differential systems with delays

Abstract

AbstractWe establish several criteria for the existence of positive periodic solutions of the multi-parameter differential systems $$\left \{ \textstyle\begin{array}{l} u'(t)+a_{1}(t)g_{1}(u(t))u(t)=\lambda b_{1}(t)f(u(t-\tau_{1}(t)),v(t-\zeta_{1}(t))), \\ v'(t)+a_{2}(t)g_{2}(v(t))v(t)=\mu b_{2}(t)g(u(t-\tau_{2}(t)),v(t-\zeta_{2}(t))), \end{array}\displaystyle \right . $${u′(t)+a1(t)g1(u(t))u(t)=λb1(t)f(u(t−τ1(t)),v(t−ζ1(t))),v′(t)+a2(t)g2(v(t))v(t)=μb2(t)g(u(t−τ2(t)),v(t−ζ2(t))), where the functions $g_{1}, g_{2}:[0,\infty)\to[0,\infty)$g1,g2:[0,∞)→[0,∞) are assumed to be unbounded. The analysis in the paper relies on the classical fixed point index theory. Our main findings improve and complement some existing results in the literature.