Abstract
We prove a weighted integral inequality of the Bessel function of zero order, which implies the positivity of the integral of the cube of nodal radial eigenfunctions of the Laplacian operator in the planar disk. This solves an open problem in Bonheure et al. (2016) and Corsato et al. (2020). The positivity plays a crucial role in transcritical bifurcation problems of nodal radial solutions of nonlinear elliptic equations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have