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On the initial value problem for two-dimensional systems of linear functional differential equations with monotone operators. (English) Zbl 1134.34038

The author gives sufficient conditions for the unique solvability of the initial value problem \(u_1(a)=c_1, u_2(a)=c_2\) for the two-dimensional differential system
\[ u'_i(t) = \sigma_{i1} l_{i1}(u_1)(t) + \sigma_{i2} l_{i2}(u_2)(t)+ q_i(t), \quad i=1,2, \]
where \(t \in[a,b],\) \(l_{ij}: C([a,b],\mathbb{R}) \to L([a,b],\mathbb{R})\) are linear nondecreasing operators, \(\sigma_{ij} \in \{-1,1\}\), \(q_i \in L([a,b],\mathbb{R}),\) and \(c_i \in \mathbb{R}, \;i,j =1,2.\)

MSC:

34K06 Linear functional-differential equations
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