Results for sixth order positively homogeneous equations

Abstract

We consider positively homogeneous the sixth order differential equations of the type x ⁽⁶⁾ = h(t, x), where hpossesses the property that h(t, cx) = ch(t, x) for c ≥ 0. This class includes the linear equations x ⁽⁶⁾ = p(t)x and piece‐wise linear ones x ⁽⁶⁾ = k ₂ x⁺ - k ₁ x⁻ . We consider conjugate points and angles associated with extremal solutions and prove some comparison results.

First published online: 14 Oct 2010