## Second order nonlinear forced oscillations.(English)Zbl 0655.34023

The author considers the following nonlinear differential equation (1) $$x''+a(t)f(x)=g(t),$$ $$t\in [0,\infty)$$, where a,g are real piecewise continuous functions on $$[0,\infty)$$; f is continuous and nondecreasing function in $$(-\infty,\infty)$$; $$xf(x)>0$$ for $$x\neq 0$$; $$h\in C^ 2[0,\infty)$$, $$h''(t)=g(t)$$ and that h(t) is oscillatory. Under another assumptions there are given sufficiently conditions under which all continuable solutions of (1) are oscillatory.
Reviewer: P.Marušiak

### MSC:

 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations 34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems

### Keywords:

superlinear equation; sublinear equation
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