Work

Localization of Critical Points in Annular Conical Sets via the Method of Nehari Manifold

Year: 2026

Type: article

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.

Source: Mediterranean Journal of Mathematics

DOI: 10.1007/s00009-026-03063-w

Author: Andrei Stan

Institutions: Babeș-Bolyai University, Tiberiu Popoviciu Institute of Numerical Analysis

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

OpenAlex ID: W7128431105