A saturation phenomenon for a nonlinear nonlocal eigenvalue problem

Francesco Della Pietra, Gianpaolo Piscitelli

Given $1\le q\le 2$ and $\alpha \in \mathbb{R}$, we study the properties of the solutions of the minimum problem \[ λ(α,q)=\min\left\{\dfrac{\displaystyle\int_{-1}^{1}|u'|^{2}dx+α\left|\i…