Systems-disconjugacy of a fourth-order differential equation with a middle term

Abstract

Systems-conjugate points were introduced and studied by Barrett [3] in relation with the self-adjoint fourth order differential equation $$ (r(x)y'')''-(q(x)y')'= p(x)y, $$ where r(x)>0, p(x)>0 and q=0. In this paper we extend some of his results to more general cases, when q(x) is free of sign restrictions.

Keywords

• Fourth-order boundary value problems
• system-conjugate points
• subwronskians
• comparison theorems