Abstract
We are proving the new oscillation theorems for the solutions of third‐order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. Our main tool is a new version of Levinson′s asymptotic theorem.
Highlights
Gro HovhannisyanAcademic Editor: Paul Eloe Copyright q 2012 Gro Hovhannisyan
Consider an ordinary nonautonomous differential equation of the third orderLv v t − 3a2 t v t 6a1 t v t 2a0 t v t 01.1 with complex valued variable coefficients a0 t, a1 t, and a2 t
In the case of real coefficients under some restrictions, we will give the criterion of oscillations of solutions of 1.2 that is invariant with respect to the adjoint transformation see Theorem 2.9 below
Summary
Academic Editor: Paul Eloe Copyright q 2012 Gro Hovhannisyan. We are proving the new oscillation theorems for the solutions of third-order linear nonautonomous differential equation with complex coefficients. In the case of real coefficients we derive the oscillation criterion that is invariant with respect to the adjoint transformation. Our main tool is a new version of Levinson’s asymptotic theorem
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