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Zbl 0879.45006
Lorenzi, Alfredo; Prilepko, Aleksey Ivanovic
Global existence results for first-order integrodifferential identification problems. (English)
[J] Rend. Semin. Mat. Univ. Padova 96, 51-84 (1996). ISSN 0041-8994

Sufficient conditions on the linear operators $A, H, H_0$ are established under which any solution $u$ to the integrodifferential equation $$u(t)= Au(t)+ \int_0^t H(t- s)Au(s)ds+ \int_0^t H_0(t-s)u(s)ds+ g(t) \tag 1$$ is positive if the pair $(g,u(0))$ is positive. Sufficient conditions for the uniqueness of the solution to the equation (1) with $g(t)= E(t)z+f(t)$ are also given and the existence in large of a unique solution is proved.
[I.Foltyńska (Poznań)]

MSC 2000:: *45N05 Integral equations in abstract spaces
45J05 Integro-ordinary differential equations
45M20 Positive solutions of integral equations

Keywords: global existence; first-order integrodifferential identification problems; positive solution; uniqueness

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