Eigenfunctions for rectangles with Neumann boundary conditions

Consider the eigenfunctions $u$ for a ree rectangular membrane wo that $-Δu=λu$ on $\mathcal R(c,d)=(0,d)\times(0,d)$. In this note we show that if if $u>0$ on $\partial \mathcal R(c,d)) then$u\equiv C$ for some positive constant.

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