×

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
PDFBibTeX XMLCite
Full Text: DOI