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

Document Type : Research Paper

Authors

Laboratory of Applied Mathematics, Faculty of Exact Sciences, University of Bejaia, 06000 Bejaia, Algeria

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

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Volume 14, Issue 10
October 2023
Pages 127-137
  • Receive Date: 22 September 2022
  • Revise Date: 17 August 2023
  • Accept Date: 19 August 2023