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


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
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