# Article

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Keywords:
Edmen-Fowler type equation of second order; oscillatory and nonoscillatory solutions; oscillatory and nonoscillatory equations
Summary:
Oscillation and nonoscillation criteria are established for the equation $$u''+p(t)|u|^{\alpha}|u'|^{1-\alpha}\operatorname{sgn} u=0,$$ where $\alpha\in ]0,1]$, and $p:[0,+\infty[\to [0,+\infty[$ is a locally summable function.
References:
[1] Fite W. B.: Concerning the zeros of the solutions of certain differential equations. Trans. Amer. Math. Soc., vol. 19 (1917), pp. 341–352. MR 1501107
[2] Hille E.: Nonoscillation theorems. Trans. Amer. Math. Soc., vol. 64 (1948), pp. 234–252. MR 0027925
[3] Del Pino M., Elgueta M., Manasevich R.: Generalized Hartman’s oscillation result for $(|x^{\prime }|^{p-2}x^{\prime })^{\prime }+c(t)|x|^{p-2}=0, p>1.$. Houston Journal of Math., vol. 17 , No 1, (1991) pp. 63–70. MR 1107187 | Zbl 0733.34039
[4] Lomtatidze A.: Oscillation and nonoscillation criteria for second order linear differential equation. Georgian Math. J., vol. 3, No. 2, (1997) pp. 129-138. MR 1439591
[5] Kiguradze I.T., Shekhter B. L.: Singular boundary value problems for second-order differential equations. in: “Current Problems in Mathematics: Newest Results”, Vol. 3, pp. 3–103, Itogi Nauki i Tekhniki, Akad. Nauk SSSR, Vsesoyuzn. Inst. Nauchn. i Tekhn. Inform., Moscow, 1987. [in Russian] MR 0925830

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