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

Andrei Stan

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arXiv · 2503.12371

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

Andrei Stan

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Abstract

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.

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Andrei Stan. 2025-03-16. Localization of critical points in annular conical sets via the method of Nehari manifold. https://arxiv.org/abs/2503.12371

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