Marino, Giuseppe; Pietramala, Paolamaria; Xu, Hong-Kun Nonlinear neutral integrodifferential equations on unbounded intervals. (English) Zbl 1167.45301 Int. Math. Forum 1, No. 17-20, 933-946 (2006). Summary: We prove the existence of solutions for a boundary value problem for a nonlinear neutral-type integrodifferential equation in \(\mathbb{R}^n\) defined on an unbounded interval. The result is obtained by using the Schaefer fixed point theorem and by using a recent result [E. De Pascale, G. Lewicki and G. Marino, Analysis, München 22, No. 1, 21–32 (2002; Zbl 1018.46014)] on the compactness of a continuous operator \(K:{\mathcal{BC}}(I,\mathbb{R}^n)\to{\mathcal{BC}}(I,\mathbb{R}^n)\); here \({\mathcal{BC}}(I,\mathbb{R}^n)\) is the Banach space of continuous functions from the (possibly) unbounded interval \(I\subset\mathbb{R}\) into \(\mathbb{R}^n\). As a corollary we obtain an existence result for solutions to a Cauchy problem for nonlinear neutral-type integrodifferential equations. Cited in 2 Documents MSC: 45J05 Integro-ordinary differential equations 34K40 Neutral functional-differential equations Citations:Zbl 1018.46014 PDFBibTeX XMLCite \textit{G. Marino} et al., Int. Math. Forum 1, No. 17--20, 933--946 (2006; Zbl 1167.45301) Full Text: DOI Link