On the strict monotonicity of the first eigenvalue of the p-Laplacian on annuli

Let B1 be a ball in RN centred at the origin and let B0 be a smaller ball compactly contained in B1. For p ∈ (1,∞), using the shape derivative method, we show that the first eigenvalue of the p-Laplacian in annulus B1\B0 strictly decreases as the inner ball moves towards the boundary of the outer ball. The analogous results for the limit cases as p → 1 and p→ ∞ are also discussed. Using our main result, further we prove the nonradiality of the eigenfunctions associated with the points on the first nontrivial curve of the Fuˇcik spectrum of the p-Laplacian on bounded radial domains