A note on a superlinear indefinite Neumann problem with multiple positive solutions

We prove the existence of three positive solutions for the Neumann problem associated to u ″ + a ( t ) u γ + 1 = 0 , assuming that a ( t ) has two positive humps and ∫ 0 T a − ( t ) d t is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.