Inserted: 19 nov 2019
Last Updated: 14 apr 2021
Journal: Comm. Partial Differential Equations
We prove that on a smooth bounded set, the positive least energy solution of the Lane-Emden equation with sublinear power is isolated. As a corollary, we obtain that the first $q-$eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the $q-$spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.
Keywords: eigenvalues, Lane-Emden equation, constrained critical points, cone condition