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On the oscillation of certain second-order differential equations. (English) Zbl 0958.34027
The authors establish new criteria for the oscillation of all solutions to second-order equations $(a(t)|x'(t)|^{\sigma-1}x'(t))+q(t)|x(t)|^\sigma \text{ sgn} x(t)=0,\quad \sigma>1,$ where the functions $$a,q:[t_0,\infty)\to{\mathbb{R}}$$ are continuous and $$a(t)>0$$ for $$t\geq t_0$$. Here, new oscillation criteria are also established for the more general equation $(a(t)|x'(t)|^{\sigma-1}x'(t))+p(t)|x'(t)|x'(t)+q(t)f(x(t))=0,\quad \sigma>1,$ where $$a,p,q:[t_0,\infty)\to{\mathbb{R}}$$, $$f:{\mathbb{R}}\to{\mathbb{R}}$$ are continuous, $$a(t)>0$$ and $$xf(x)>0$$ for $$u\neq 0$$.

##### MSC:
 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations
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