On periodic solutions of two-dimensional nonautonomous differential systems Original Research Article

Nonimprovable conditions are established for the existence and uniqueness of an ωω-periodic solution of the nonautonomous differential systems View the MathML sourceui′=pi1(t)u1+pi2(t)u2+qi(t)(i=1,2) Turn MathJax on and View the MathML sourceui′=fi(t,u1,u2)(i=1,2), Turn MathJax on where pik:R→Rpik:R→R, qi:R→Rqi:R→R(i,k=1,2)(i,k=1,2) are ωω-periodic functions, Lebesgue integrable on [0,ω][0,ω], and fi:R×R2→Rfi:R×R2→R(i=1,2)(i=1,2) are functions from the Carathéodory class such that View the MathML sourcefi