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Oscillatory properties of fourth order self-adjoint differential equations

Simona Fišnarová — 2004

Archivum Mathematicum

Oscillation and nonoscillation criteria for the self-adjoint linear differential equation ( t α y ' ' ) ' ' - γ 2 , α t 4 - α y = q ( t ) y , α ∉ { 1 , 3 } , where γ 2 , α = ( α - 1 ) 2 ( α - 3 ) 2 16 and q is a real and continuous function, are established. It is proved, using these criteria, that the equation t α y ' ' ' ' - γ 2 , α t 4 - α + γ t 4 - α ln 2 t y = 0 is nonoscillatory if and only if γ ≤ α 2 - 4 α + 5 8 .

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