On positive periodic solutions of second-order semipositone differential equations

Abstract

Using the Krasnosel’skii’s fixed point theorem, we establish the existence and multiplicity of positive Tperiodicsolutions of second-order semipositone system $x''(t)+a(t)x(t)=lambda f(t,x(t)),x(0)=x(T),x'(0)=x'(T)$ where $x=(x_1,;x_2,......,;x_n),;f(t,x)=(f_1(t,x),;f_2(t,x),.....,;f_n(t,x))$ is bounded below.