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.
A note on a superlinear indefinite Neumann problem with multiple positive solutions
BOSCAGGIN, Alberto
2011-01-01
Abstract
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.
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