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 (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.
Positive solutions to the sublinear Lane-Emden equation are isolated
Franzina G
2021
Abstract
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 (Formula presented.) eigenvalue of the Dirichlet-Laplacian is not an accumulation point of the (Formula presented.) spectrum, on a smooth bounded set. Our results extend to a suitable class of Lipschitz domains, as well.File in questo prodotto:
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