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Zbl 1156.34338
Bobrowski, Adam; Kubalińska, Ma\l{}gorzata
On a functional equation with derivative and symmetrization. (English)
[J] Ann. Pol. Math. 89, No. 1, 13-24 (2006). ISSN 0066-2216; ISSN 1730-6272/e

Summary: We study existence, uniqueness and form of solutions to the equation $\alpha g - \beta g' + \gamma g_{\text {e}} = f$ where $\alpha, \beta, \gamma$ and $f$ are given, and $g_{\text {e}}$~stands for the even part of a searched-for differentiable function $g$. This equation emerged naturally as a result of the analysis of the distribution of a certain random process modelling a population genetics phenomenon.

MSC 2000:: *34K06 Linear functional-differential equations
92D10 Genetics
47D06 One-parameter semigroups and linear evolution equations

Keywords: functional equation; differential equation; Cauchy problem; semigroups of operators; genetic drift

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