Mixed local and nonlocal eigenvalues

We discuss some basic properties of eigenfunctions for a class of mixed local and nonlocal operators whose prototype is $-{\Delta }_{p}u-{(-{\Delta }_p)}^{s}u=\lambda {\left|u\right|}^{p-2}u,$ for any summability exponent $p\in (1,\infty )$ and any differentiability order $s\in (0,1)$.