This paper presents sufficient conditions for the existence of positive solutions to a class of nonlinear integral inclusion of the form
where is a single valued map, is the set of selections of the multivalued map and . These results are obtained via a fixed point theorem due to M. Martelli [Boll. Unione Mat. Ital., IV. Ser. 11, Suppl. Fasc. 3, 70–76 (1975; Zbl 0314.47035)] or the author [S. Hong, Electron. J. Differ. Equ. 2003, Paper No. 32 (2003; 1023.34056)] for condensing multivalued maps on ordered Banach spaces.