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Zbl 0862.45006
O'Regan, Donal
Existence results for nonlinear integral equations on the half line.
(English)
[A] Corduneanu, C. (ed.), Qualitative problems for differential equations and control theory. Dedicated to Aristide Halanay on occasion of his 70th birthday. Singapore: World Scientific. 121-131 (1995). ISBN 981-02-2257-2/hbk

The paper deals with integral equations on the positive half-axis $$y(t)= h(t)+\int^t_0 k_1(t,s)f_1(s,x(s))ds+ \int^\infty_0 k_2(t,s)f_2(s,x(s))ds,\tag E$$ under suitable conditions to secure the existence of at least one solution. The method is based on the Schauder-Tikhonov fixed point theorem in the space of continuous maps from $[0,\infty)$ into $\bbfR^n$, with the topology of uniform convergence on finite intervals. The author also applies a continuation theorem due to {\it M. Furi} and {\it M. P. Pera} [Pac. J. Math. 160, No. 2, 219-244 (1993; Zbl 0784.58050)]. In particular, existence of bounded solutions is secured for the equation (E).
[C.Corduneanu (Arlington)]
MSC 2000:
*45G05 Singular nonlinear integral equations

Keywords: nonlinear integral equations on the half line; Schauder-Tikhonov fixed point theorem; bounded solutions

Citations: Zbl 0784.58050

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