Localization of critical points in annular conical sets via the method of Nehari manifold

Fuente: arXiv
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Autore principale: Stan, Andrei
Natura: Preprint
Pubblicazione: 2025
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author Stan, Andrei
author_facet Stan, Andrei
contents Using the Nehari manifold method, we establish sufficient conditions such that a smooth functional attains a ground state within an annular domain of a closed cone. The localization we obtain immediately allows for multiplicity when applied to disjoint conical sets. To illustrate our results, we consider a two-point boundary value problem and obtain a solution within a shell of a closed cone, defined in terms of a Harnack inequality with respect to the energy norm. The conditions imposed on the nonlinear term naturally extend those from classical examples in the literature which were derived using the method of Nehari manifold on the entire domain.
format Preprint
id arxiv_https___arxiv_org_abs_2503_12371
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Localization of critical points in annular conical sets via the method of Nehari manifold
Stan, Andrei
Analysis of PDEs
Functional Analysis
Using the Nehari manifold method, we establish sufficient conditions such that a smooth functional attains a ground state within an annular domain of a closed cone. The localization we obtain immediately allows for multiplicity when applied to disjoint conical sets. To illustrate our results, we consider a two-point boundary value problem and obtain a solution within a shell of a closed cone, defined in terms of a Harnack inequality with respect to the energy norm. The conditions imposed on the nonlinear term naturally extend those from classical examples in the literature which were derived using the method of Nehari manifold on the entire domain.
title Localization of critical points in annular conical sets via the method of Nehari manifold
topic Analysis of PDEs
Functional Analysis
url https://arxiv.org/abs/2503.12371