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Existence of solutions for a class of first order boundary value problems

Amirouche Mouhous a;  Svetlin Georgiev Georgiev b;  Karima Mebarki c — 2022

Archivum Mathematicum

In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.

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

Lydia Bouchal a;  Karima Mebarki a;  Svetlin Georgiev Georgiev b — 2022

Archivum Mathematicum

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.

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