Oscillation and nonoscillation of solutions to even order self-adjoint differential equations
Date
2003-11-25
Authors
Dosly, Ondrej
Fisnarova, Simona
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
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
Description
Keywords
Self-adjoint differential equation, Variational methods, Oscillation and nonoscillation criteria, Conditional oscillation
Citation
Dosly, 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.
Rights
Attribution 4.0 International