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Annali di Matematica Pura ed Applicata

, Volume 106, Issue 1, pp 171–185 | Cite as

Nonlinear oscillation of second order differential equations with retarded argument

  • Takaŝi Kusano
  • Manabu Naito
Article

Summary

Oscillation and nonoscillation theorems are presented for the nonlinear retarded differential equation
$$[r(t)x'(t)]' + x\left( (g(t)) \right)F\left( ([x\left( (g(t)) \right)]^2 ,t) \right) = 0 \left( (r(t) > 0) \right)$$
(A)
where\(\mathop \smallint \limits^\infty r^{-1} (t)dt< \infty\). The results obtained show that there is a remarkable difference between the oscillatory property of(A) in the case\(\mathop \smallint \limits^\infty r^{-1} (t)dt< \infty\) and that of(A) in the case\(\mathop \smallint \limits^\infty r^{-1} (t)dt = \infty\).

Keywords

Differential Equation Remarkable Difference Nonlinear Oscillation Order Differential Equation Oscillatory Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1975

Authors and Affiliations

  • Takaŝi Kusano
    • 1
  • Manabu Naito
    • 1
  1. 1.HiroshimaJapan

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