Maximum and antimaximum principles near the second eigenvalue
Maximum and antimaximum principles near the second eigenvalue
We consider the Dirichlet problem $ (*)$ $-\Delta u = \mu u + f $ in $\Omega$, $u=0$ on $\partial \Omega$, with $\Omega$ either a bounded smooth convex domain in $\mathbb R^2$, or a ball or an annulus in $\mathbb R^N$. Let $\lambda_2$ be the second eigenvalue, with $\varphi_2$ an …