Fixed point theorem on functional intervals for sum of two operators and application in ODEs

Author(s):

Lydia Bouchal * , Karima Mebarki

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
In this paper, we present a generalization of the functional expansion-compression fixed point theorem developed by Avery et al. in [5] to the case of a k-set contraction perturbed by an operator T, where I -T is Lipschitz invertible. The arguments are based upon recent fixed point index theory in cones of Banach spaces. Next, we apply the obtained result to discuss the existence of a nontrivial positive solution to a nonautonomous second order boundary value problem.
Keywords:

Fixed point , Sum of operators , positive solution , fixed point index , cones

Language:
English
Published:
International Journal Of Nonlinear Analysis And Applications, Volume:14 Issue: 10, Oct 2023
Pages:
127 to 137
https://www.magiran.com/p2639612