Comparison Theorems for Fourth Order Differential Equations Garret
نویسندگان
چکیده
This paper establishes an apparently overlooked relationship between the iv yiV p'air of fourth order line,r equations y p(x)y 0 and + p(x)y 0, where p is , positive, continuous function defined on [O,m). It is shown that if all solutions of the first equation are nonoscillatory, then all solutions of the second equation must be nonoscillatory as well. An oscillation criterion for these equations is also given.
منابع مشابه
Comparison Theorems for Half-linear Differential Equations of the Fourth Order
An identity of the Picone type for fourth-order half-linear ordinary differential operators of the form lα[x] ≡ (pφ(x′′))′′ − (rφ(x′))′ + qφ(x) and Lα[y] ≡ (Pφ(y′′))′′ − (Rφ(y′))′ +Qφ(y). where φ(u) := |u|α−1u, α > 0, u ∈ 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 ...
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