A Nehari manifold method for nonvariational problems

2025/12/04 by Radu Precup, Precup, Radu, Andrei Stan +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fixed Point Theorems Analysis #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2512.05055

openalex publication_date 2025/12/04 · openalex created_date 2025/12/06 · openalex updated_date 2026/07/28

Abstract

The aim of this paper is to extend the Nehari manifold method from the variational setting to the nonvariational framework of fixed point equations. This is achieved by constructing a radial energy functional that generalizes the standard one from the variational case. Furthermore, the solutions obtained through our method are localized in conical annular sets, which leads to the existence of multiple solutions. The abstract results are illustrated by two representative applications.

Citations

• Hybrid Nehari-Schauder type fixed point results and applications
• Critical point localization and multiplicity results in Banach spaces via Nehari manifold technique
• Localization of critical points in annular conical sets via the method of Nehari manifold
• Nehari manifold optimization and its application for finding unstable solutions of semilinear elliptic PDEs
• Ground states of elliptic problems over cones

Related

• Hybrid Nehari-Schauder type fixed point results and applications
• Localization of critical points in annular conical sets via the method of Nehari manifold
• Critical point localization and multiplicity results in Banach spaces via Nehari manifold technique
• Further applications of the Nehari manifold method to functionals in C¹(X ∖ \0\)
• Some applications of the Nehari manifold method to functionals in C¹(X ∖ \0\)