p. 271 - 276 Comparison theorems for half-linear differential equations
of the fourth order J. Jaroš 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 - 1}u, 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 l_{α}[x] = 0 and L_{α}[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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