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 $u'' + a(t)u^{\gamma+1} = 0$, assuming that $a(t)$ has two positive humps and $\int_0^T a^-(t)\, dt$ is large enough. Actually, the result holds true for a more general class of superlinear nonlinearities.