Positive solutions for a class of non-autonomous second order difference equations via a new functional fixed point theorem

Bouchal, Lydia   ; Mebarki, Karima   ; Georgiev b , Svetlin Georgiev

Archivum mathematicum, Tome 58 (2022) no. 4, pp. 199-211

Abstract (VO)

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.

Détail

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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