Two-Parametric Conditionally Oscillatory Half-Linear Differential Equations

Ondřej DoÅ¡lý and Simona FiÅ¡narová

Abstract and Applied Analysis, 2011, vol. 2011, 1-16

Abstract:

We study perturbations of the nonoscillatory half-linear differential equation ( ð ‘Ÿ ( ð ‘¡ ) Φ ( ð ‘¥ ′ ) ) ′ + ð ‘ ( ð ‘¡ ) Φ ( ð ‘¥ ) = 0 , Φ ( ð ‘¥ ) ∶ = | ð ‘¥ | ð ‘ âˆ’ 2 ð ‘¥ , ð ‘ > 1 . We find explicit formulas for the functions Ì‚ ð ‘Ÿ , Ì‚ ð ‘ such that the equation [ ( ð ‘Ÿ ( ð ‘¡ ) + 𠜆 Ì‚ ð ‘Ÿ ( ð ‘¡ ) ) Φ ( ð ‘¥ ′ ) ] ′ + [ ð ‘ ( ð ‘¡ ) + 𠜇 Ì‚ ð ‘ ( ð ‘¡ ) ] Φ ( ð ‘¥ ) = 0 is conditionally oscillatory, that is, there exists a constant ð ›¾ such that the previous equation is oscillatory if 𠜇 − 𠜆 > ð ›¾ and nonoscillatory if 𠜇 − 𠜆 < ð ›¾ . The obtained results extend the previous results concerning two-parametric perturbations of the half-linear Euler differential equation.

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:182827

DOI: 10.1155/2011/182827

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