Rotation properties of a class of second order differential systems

Comparison Theorems for a Class of Selfadjoint Fourth Order Differential Equations

“…The purpose of this paper is to present such comparison theorems in the more general context of the rotation theory developed in [2]. This will enable us to simplify some arguments and also to fill a gap in the proof of Theorem 10.2 of [1].…”

Comparison theorems for a class of selfadjoint fourth order differential equations

“…Suppose to the contrary that there exists a y > a such that 9(y) = 0(y) (mod it). Then by Lemma 2.1 of [2] there exist nontrivial constants X, p such that z(x) = Xz(x) + pZ(x); y(x) = Xy(x) + pY(x) satisfies (1.2) and z(y) = y(y) = 0. The corresponding area function therefore satisfies tp(y) = 0, and since <p'(x) > 0, we have <p(a) < 0.…”

“…The purpose of this paper is to present such comparison theorems in the more general context of the rotation theory developed in [2]. This will enable us to simplify some arguments and also to fill a gap in the proof of Theorem 10.2 of [1].…”

“…The advantage of the latter form is that it enables us to interpret conjugate points and oscillation properties in terms of the rotation theory developed in [2]. Some basic ideas and results from this theory are presented in the following section.…”

“…As explained in [2], we may assume without loss of generality that 90 = 0, so that the initial conditions imply so that e*K+I) > 0o + 2^ = e*( ßk).…”