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Zbl 0823.34039
Takaŝi, Kusano; Yoshida, Norio
Nonoscillation theorems for a class of quasilinear differential equations of second order. (English)
[J] J. Math. Anal. Appl. 189, No.1, 115-127 (1995). ISSN 0022-247X

The ordinary differential equation $(\vert y' \vert\sp{\alpha - 1} y')' + q(t) \vert y \vert\sp{\beta - 1} y = 0$, $t \ge a$, is considered for $\alpha$ and $\beta$ positive but with $\alpha \ne 1$. If $\alpha = 1$ then the equation is the Emden-Fowler equation. The main theorem proved is the following: all solutions of the differential equation with $\alpha \ne \beta$ are nonoscillatory if $$\int\sp \infty\sb a {\bigl( q'(t) \bigr)\sb + \over q(t)} dt < \infty, \quad \text {and} \quad \int\sp \infty\sb a t\sp \gamma q(t)dt < \infty,$$ where $(q'(t))\sb + = \max \{q'(t), 0\}$ and $\gamma = \max \{\alpha, \beta\}$.
[P.Smith (Keele)]

MSC 2000:: *34C10 Qualitative theory of oscillations of ODE: Zeros, etc.

Keywords: Emden-Fowler equation; nonoscillatory

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