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Comparison theorems for half-linear differential equations
of the fourth order
Received: January 9, 2011; Accepted: May 23, 2011
Abstract. An identity of the Picone type for fourth-order half-linear ordinary differential operators of the form
where φ(u) := |u|α - 1u, α > 0, u Î R, and p, q, r, P, Q and R are continuous functions on a given interval I is derived and then Sturmian comparison theory for the corresponding fourth-order equations lα[x] = 0 and Lα[y] = 0 based on this identity is developed.
Keywords: Picone's identity; half-linear differential equation; fourth order.
AMS Subject classification: Primary: 34C10
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