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Conditionally oscillatory half-linear differential equations

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Abstract

We consider a nonoscillatory half-linear second order differential equation

$$ (r(t)\Phi (x'))' + c(t)\Phi (x) = 0,\Phi (x) = \left| x \right|^{p - 2} x,p > 1, $$
((*))

and suppose that we know its solution h. Using this solution we construct a function d such that the equation

$$ (r(t)\Phi (x'))' + [c(t) + \lambda d(t)]\Phi (x) = 0 $$
((**))

is conditionally oscillatory. Then we study oscillations of the perturbed equation (**). The obtained (non)oscillation criteria extend existing results for perturbed half-linear Euler and Euler-Weber equations.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Masaryk University, Janáčkovo nám. 2a, CZ-602 00, Brno, Czech Republic

    O. Došlý

  2. Faculty of Engineering, Bahcesehir University, TR-34100, Besiktas, Istanbul, Turkey

    M. Ünal

Authors
  1. O. Došlý
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  2. M. Ünal
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Correspondence to O. Došlý.

Additional information

Research supported by the grant 201/07/0145 of the Grant Agency of the Czech Republic and by the Research Project MSM0021622409 of the Ministry of Education of the Czech Government.

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Došlý, O., Ünal, M. Conditionally oscillatory half-linear differential equations. Acta Math Hung 120, 147–163 (2008). https://doi.org/10.1007/s10474-007-7120-4

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  • DOI: https://doi.org/10.1007/s10474-007-7120-4

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