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Oscillation and nonoscillation of half-linear Euler type differential equations with different periodic coefficients

Adil Misir, Banu Mermerkaya (2017)

Open Mathematics

In this paper, we compute explicitly the oscillation constant for certain half-linear second-order differential equations having different periodic coefficients. Our result covers known result concerning half-linear Euler type differential equations with α-periodic positive coefficients. Additionally, our result is new and original in case that the least common multiple of these periods is not defined. We give an example and corollaries which illustrate cases that are solved with our result.

Oscillation and nonoscillation of higher order self-adjoint differential equations

Ondřej Došlý, Jan Osička (2002)

Czechoslovak Mathematical Journal

Oscillation and nonoscillation criteria for the higher order self-adjoint differential equation ( - 1 ) n ( t α y ( n ) ) ( n ) + q ( t ) y = 0 ( * ) are established. In these criteria, equation ( * ) is viewed as a perturbation of the conditionally oscillatory equation ( - 1 ) n ( t α y ( n ) ) ( n ) - μ n , α t 2 n - α y = 0 , where μ n , α is the critical constant in conditional oscillation. Some open problems in the theory of conditionally oscillatory, even order, self-adjoint equations are also discussed.

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