Functional differential equations of mixed type in Banach spaces. (English) Zbl 0851.34076
The author studies existence, uniqueness and dependence on boundary conditions for the functional differential equation of mixed type \(x'(t)= f(t, x(t), x(t+ \tau(t))\), \(x(t- \tau(t)))\) for a.e. \(t\in(\alpha, \beta)\), in a Banach space \(B\), with boundary conditions \(x(t)= \varphi(t)\), \(t\in [\alpha- s, \alpha]\), \(x(t)= \psi(t)\), \(t\in [\beta, \beta+ s)\), where \(\tau(\cdot)\) is a continuous function, \(0\leq r\leq \tau(t)\leq s\) and \(f: (\alpha, \beta)\times B\times B\times B\to B\) is strongly measurable in \(t\) and satisfies a Lipschitz condition in \((x, y, z)\in B\times B\times B\).
Reviewer: T.-D.Havarneanu (Iaşi)
MSC:
| 34K30 | Functional-differential equations in abstract spaces |
Keywords:
existence; uniqueness; dependence on boundary conditions; functional differential equation of mixed type; Banach spaceReferences:
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