Oscillation and nonoscillation of solutions to even order self-adjoint differential equations
Abstract
We establish oscillation and nonoscilation criteria for the linear differential equation
(-1)n (tαy(n))(n) - γn,α/ t2n-α y = q(t)y, α ∉ {1, 3, ..., 2n - 1},
where
γn,α = 1/ 4n Πnk=1 (2k - 1 - α)2
and q is a real-valued continuous function. It is proved, using these criteria, that the equation
(-1)n (tαy(n))(n) - (γn,α/ t2n-α + γ/ t2n-α lg2t) y = 0
is nonoscillatory if and only if
γ ≤ ~γn,α := 1/ 4n ∏nk=1 (2k - 1 - α)2 ∑nk=1 1/ (2k - 1 - α)2
Citation
Dosly, O., & Fisnarova, S. (2003). Oscillation and nonoscillation of solutions to even order self-adjoint differential equations. Electronic Journal of Differential Equations, 2003(115), pp. 1-21.Rights License

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