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On boundedness and stability of solutions of second order linear differential equations with advanced arguments. (English) Zbl 0926.34061

The authors consider linear differential equations with advanced arguments \[ u''(t) + \sum_{k=1}^{n}l_k(t) u(\tau_k(t))=0,\tag{1} \] with \(\tau_k\geq t\) for \(t\geq 0\). The main result presents conditions under which equation (1) has a two-dimensional space of bounded and in a certain sense stable solutions. An asymptotic representation of these solutions is given.

MSC:

34K20 Stability theory of functional-differential equations
34K25 Asymptotic theory of functional-differential equations
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