Geodesic
Some oscillation theorems for second order differential equations
Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 845-861
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In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation \[ (r(t)\Phi (u^{\prime }(t)))^{\prime }+c(t)\Phi (u(t))=0, \] where (i) $r,c\in C([t_{0}, \infty )$, $\mathbb{R}:=(-\infty , \infty ))$ and $r(t)>0$ on $[t_{0},\infty )$ for some $t_{0}\ge 0$; (ii) $\Phi (u)=|u|^{p-2}u$ for some fixed number $p> 1$. We also generalize some results of Hille-Wintner, Leighton and Willet.
In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation \[ (r(t)\Phi (u^{\prime }(t)))^{\prime }+c(t)\Phi (u(t))=0, \] where (i) $r,c\in C([t_{0}, \infty )$, $\mathbb{R}:=(-\infty , \infty ))$ and $r(t)>0$ on $[t_{0},\infty )$ for some $t_{0}\ge 0$; (ii) $\Phi (u)=|u|^{p-2}u$ for some fixed number $p> 1$. We also generalize some results of Hille-Wintner, Leighton and Willet.
Classification : 34C10, 34C15
Keywords: oscillatory; nonoscillatory; Riccati differential equation; Sturm Comparison Theorem 
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Lee, Chung-Fen; Yeh, Cheh-Chih; Gau, Chuen-Yu. Some oscillation theorems for second order differential equations. Czechoslovak Mathematical Journal, Tome 55 (2005) no. 4, pp. 845-861. http://geodesic.mathdoc.fr/item/CMJ_2005_55_4_a2/

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