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. ![Creative Commons License](https://i.creativecommons.org/l/by/4.0/80x15.png)
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