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In this paper, we prove new compression–expansion type fixed point theorems in cones for the so-called decomposable maps, that is, compositions of two upper semicontinuous multivalued maps. As an application, we obtain existence and localization of positive solutions for a differential equation with    $$\phi $$  ϕ -Laplacian and discontinuous nonlinearity subject to multi-point boundary conditions. As far as we are aware, the existence results are new even in the classical case of continuous nonlinearities.

Compression–Expansion Fixed Point Theorems for Decomposable Maps and Applications to Discontinuous $$\phi $$-Laplacian problems