Note on a nonlinear eigenvalue problem
Consider the nonlinear eigenvalue problem \({d \over dx} (| u' |^{p-2}u')+ \lambda | u |^{p-2}u=0\). It is observed that the first positive eigenvalue \(\lambda_ p\) satisfies a conjugacy condition \(\lambda_ p^{1/p}=\lambda_ q^{1/p}\), \({1 \over p} + {1 \over q}=1\). Also the corresponding eigenfunctions are related. Similar results hold for the higher eigenvalues and eigenvectors.
scientific article; zbMATH DE number 218645