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Stability and square integrability of solutions of nonlinear third order differential equations. (English) Zbl 1326.34088

From the introduction: We investigate some asymptotic properties of solutions of the third-order nonlinear differential equation \[ [P(x(t))x'(t)]''+ a(t)(Q(x(t))x'(t))'+ b(t)(R(x(t))x'(t))+ c(t) f(x(t))=0, \] where the functions \(a,b,c:[0,\infty)\to [0,\infty)\), \(P,Q,R:\mathbb{R}\to [0,\infty)\), and \(f:\mathbb{R}\mathbb{R}\) are continuous, and \(xf(x)>0\) for \(x\neq 0\).

MSC:

34D20 Stability of solutions to ordinary differential equations
34C11 Growth and boundedness of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
34D23 Global stability of solutions to ordinary differential equations
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