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A theorem on the spectral radius of the sum of two operators and its application. (English) Zbl 0795.34069

A theorem on existence of solution to the neutral differential equation \[ x'(t)= f(t,x(h(t)),x'(H(t))), \qquad t\in [0,T], \quad x(0)=0, \] \(f\) Lipschitzian in \(x\), \(x'\), \(h(H(t))\leq h(t)\leq t\), is demonstrated. The demonstration is based on a fixed point theorem in partially ordered spaces given by the authoress. Some new properties of the spectral radius, essential in the paper, are demonstrated.

MSC:

34K40 Neutral functional-differential equations
47H10 Fixed-point theorems
47A10 Spectrum, resolvent
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References:

[1] Zima, Bull. Austral. Math. Soc. 46 pp 179– (1992)
[2] Tsamatos, Fasc. Math. 14 pp 63– (1985)
[3] Riesz, Functional analysis (1955)
[4] DOI: 10.1002/mana.19901450120 · Zbl 0762.65046 · doi:10.1002/mana.19901450120
[5] Deimling, Nonlinear functional analysis (1985) · doi:10.1007/978-3-662-00547-7
[6] Banaś, Folia. Scientiarum Universitatis Technicae Resoviensis 34 (1987)
[7] Krasnosel’skii, Approximate solution of operator equations (1972) · doi:10.1007/978-94-010-2715-1
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