Consider the coupled system
where , for , can be singular at .
The authors assume that the Green’s function belonging to the boundary value problem
is nonnegative and that the function satisfies
for and , where .
Under additional conditions on the maximum and minimum of the function
they prove the existence of positive solutions of satisfying periodic boundary conditions. Since there is no assumption on the -periodicity of the functions and with respect to , the solutions are not necessarily -periodic solutions.