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Zbl 1027.34040
Rogovchenko, Svitlana P.; Rogovchenko, Yuri V.
Oscillation theorems for differential equations with a nonlinear damping term.
(English)
[J] J. Math. Anal. Appl. 279, No.1, 121-134 (2003). ISSN 0022-247X

The authors investigate oscillatory properties of the nonlinear second-order differential equation $$(r(t)k_1(x,x'))' +p(t)k_2(x,x')x'+q(t)f(x)=0,\tag *$$ under natural restrictions on the functions $r,k_1,k_2,p,q$ and $f$. Using a modified $H$-function averaging technique introduced for linear equations by {\it Ch. G. Philos} [Arch. Math. 53, 482-492 (1989; Zbl 0661.34030)], additional conditions are found which guarantee that (*) possesses no nonoscillatory solution. The results of the paper are illustrated by a number of examples showing that the obtained criteria apply in situations where known criteria fail.
[Ondřej Došlý (Brno)]
MSC 2000:
*34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: nonlinear differential equations; nonlinear damping term; proper solutions; integral averaging method

Citations: Zbl 0661.34030

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