Geodesic
Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem
Archivum mathematicum, Tome 58 (2022) no. 4, pp. 199-211.

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In this paper, by using recent results on fixed point index, we develop a new fixed point theorem of functional type for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ a $k$-set contraction. This fixed point theorem is then used to establish a new result on the existence of positive solutions to a non-autonomous second order difference equation.
DOI : 10.5817/AM2022-4-199
Classification : 39A27, 47H10
Keywords: fixed point; sum of operators; non-autonomous difference equations; positive solution 
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     title = {Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem},
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Bouchal, Lydia; Mebarki, Karima; Georgiev b , Svetlin Georgiev. Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem. Archivum mathematicum, Tome 58 (2022) no. 4, pp. 199-211. doi : 10.5817/AM2022-4-199. http://geodesic.mathdoc.fr/articles/10.5817/AM2022-4-199/

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