Consider the weighted p(t)-Laplacian ordinary system - (w(t)|u'(t)|p(t)-2u'(t))'+w(t)f(t,u(t))=0 in (a, b), u(a)=u(b)=0, where f ∈C([a, b]×RN, RN), w∈C([a, b], R), p∈C([a, b], R) and p(t)>1 for t∈[a, b]. It is proved that if R>0 such that 〈f(t, u), u〉≥0, t∈[a, b], u∈RN with |u|=R, then the problem has a solution u such that |u(t)|≤R for t∈[a, b]. As a corollary of this result, taking w(t)=tn-1, we obtain the existence of the radial solutions for the elliptic systems. Our result generalized the corresponding results obtained by Hartman and Mawhin.