MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
NEW MULTIPLE FIXED POINT THEOREMS FOR SUM OF TWO OPERATORS AND APPLICATION TO A SINGULAR GENERALIZED STURM-LIOUVILLE MULTIPOINT BVP
L. Bouchal, K. Mebarki

Abstract

In this paper, we develop some new multiple fixed point theorems for the sum of two operators $T+S$ where $I-T$ is Lipschitz invertible and $S$ is a $k$-set contraction on translate of a cone in a Banach space. New existence criteria for multiple positive solutions of a singular generalized Sturm-Liouville multipoint boundary value problem are established. The article ends with an illustrative example.

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Keywords: Fixed point; sum of operators; cone; Sturm-Liouville BVP; multiple positive solutions.

MSC: 47H10, 34B10, 34B24

DOI: 10.57016/MV-38FENT80

Pages:  196--209     

Volume  76 ,  Issue  3 ,  2024