Discussion on the analytic solutions of the second-order iterated differential equation
Bull. Korean Math. Soc. 2006 Vol. 43, No. 4, 791-804
Printed December 1, 2006
Han Ze Liu and Wen Rong Li
Binzhou University
Abstract : This paper is concerned with a second-order iterated differential equation of the form $c_{0}x''(z)+c_{1}x'(z)+c_{2}x(z)=x(az+bx(z))+h(z)$ with the distinctive feature that the argument of the unknown function depends on the state. By constructing a convergent power series solution of an auxiliary equation, analytic solutions of the original equation are obtained.
Keywords : iterative functional differential equation, analytic solution, majorant series
MSC numbers : 39B12, 30D05
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