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 h possesses 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.

Key words:

• differential equations of 6‐th order
• equations with asymmetric nonlinearities
• conjugate points
• positive homogeneous equations

Notes

Supported by ESF project Nr. 2004/0003/VPD1/ESF/PIAA/04/NP/3.2.3.1./0003/0065