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Systems-conjugate points have been introduced and studied by John Barrett\cite{barr} in relation with the self-adjoint fourth order differentialequation $$(r(x)y")"-(q(x)y')'= p(x)y,$$ where $r(x)>0$, $p(x)>0$ and$q\equiv0$. In this paper we extend some of his results to more general cases,when $q(x)$ is free of any sign restrictions.

Systems-Disconjugacy of a Fourth-Order Differential Equation with a Middle Term