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Integral averages and oscillation of second-order nonlinear differential equations

✍ Scribed by J.V. Manojlović

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
813 KB
Volume
41
Category
Article
ISSN
0898-1221

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✦ Synopsis

we present some criteria for the oscillation of the second-order nonlinear differential equation [a(+Sr(t))z'(t)] + z#)z'(t) + &)f(z(t)) = 0, t L to > 0, where a E C'( [to, 00)) is a,nonnegative function, q E C( [to, 00)) are allowed to change sign on [to, co), @, f E C'(B;R), $(z) > 0, zf(z) > 0, f'(z) 1 0 for z # 0. These criteria are obtained by using a general class of the parameter functions H(t, s) in the averaging techniques and represent extension, ss well as improvement of known oscillation criteria of Philos and Purnarae for the generalized Emden-Fowler equation.

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