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An existence result for positive solutions to a fourth order differential inclusion with boundary values is given. This is accomplished by using a fixed point theorem on cones for multivalued maps, L1 selections and a generalization of the Ascoli theorem. The inclusion allows the function and its first three derivatives to be on the right-hand side. The proof involves a Green’s function and a positive eigenvalue of a particular operator. An example is provided. Mathematics subject classification (2010): 34B18, 34A34, 34A36, 34A60, 34B15, 47H10.

Positive solutions for a fourth order differential inclusion based on the Euler-Bernoulli equation for a Cantilever beam