2005, 2005(Special): 730-737. doi: 10.3934/proc.2005.2005.730

Unique summing of formal power series solutions to advanced and delayed differential equations

1. 

Department of Mathematics, East Carolina University, Greenville, NC 27858, United States, United States

Received  September 2004 Revised  May 2005 Published  September 2005

The analytic delayed-differential equation $z^2 \psi ^{\ \! \prime } (z) \ + \ \psi (z/q) \ = \ z$ for $q>1$ has a solution which can be expressed as a formal power series. A $q$-advanced Laplace-Borel kernel provides for the construction of an analytic solution whose domain is the right half plane with vertex at the initial point $z=0$. This method is extended to provide a continuous family of solutions, of which a subfamily extends to a punctured neighborhood of $z=0$ on the logarithmic Riemann surface. Conditions are given on the asymptotics of $\psi ^{\ \! \prime } (z)$ near $z=0$ to ensure uniqueness.
Citation: David W. Pravica, Michael J. Spurr. Unique summing of formal power series solutions to advanced and delayed differential equations. Conference Publications, 2005, 2005 (Special) : 730-737. doi: 10.3934/proc.2005.2005.730
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