Dosly, OndrejFisnarova, Simona2021-01-292021-01-292003-11-25Dosly, O., & Fisnarova, S. (2003). Oscillation and nonoscillation of solutions to even order self-adjoint differential equations. <i>Electronic Journal of Differential Equations, 2003</i>(115), pp. 1-21.1072-6691https://hdl.handle.net/10877/13166We 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)2Text21 pages1 file (.pdf)enAttribution 4.0 InternationalSelf-adjoint differential equationVariational methodsOscillation and nonoscillation criteriaConditional oscillationArticle