Geodesic
A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients
Trudy Instituta matematiki, Tome 32 (2024) no. 1, pp. 74-85

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The paper provides an existence criterion and a complete description of continuos solutions $f\colon\mathbb R\to \mathbb R$ of the linear second-order functional equation $f(f(x))+af(x)+bx=0$ with constant coefficients.
Keywords: linear functional equation, trajectory approach, one-dimensional dynamics, linear recurrent sequences. 
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     title = {A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients},
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M. V. Karpuk; P. A. Khudziakova. A complete description of continuous on the real line solutions of the linear functional equation of the second order with constant coefficients. Trudy Instituta matematiki, Tome 32 (2024) no. 1, pp. 74-85. http://geodesic.mathdoc.fr/item/TIMB_2024_32_1_a8/