A Two-Point Boundary Problem for Ordinary Self-Adjoint Differential Equations of Fourth Order

Abstract

The purpose of this note is to establish Theorem A below for the two-point homogeneous vector boundary problem where the P i ( x ) are given real m × m symmetric matrix functions of x with P 0 ( x ) positive definite and P i ( x ) of class C 2−i on an infinite interval [ a , ∞), and where by a solution of (1.1) — (1.2) for a ≤ x 1 < x 2 < ∞ we understand a real m-dimensional column vector u = u ( x ) of class C 2 on [ a , ∞) which is such that P i (x)u( 2−i ) is of class C 2−i on [ a , ∞) and which satisfies (1.1) — (1.2) with the former a vector identity on [ a , ∞).