×

Nonlinear neutral integrodifferential equations on unbounded intervals. (English) Zbl 1167.45301

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.

MSC:

45J05 Integro-ordinary differential equations
34K40 Neutral functional-differential equations

Citations:

Zbl 1018.46014
PDFBibTeX XMLCite
Full Text: DOI Link