2024 Partial minimization over the Nehari set and applications to elliptic equations
Omar Cabrera Chavez
Topol. Methods Nonlinear Anal. 63(2): 559-593 (2024). DOI: 10.12775/TMNA.2023.031

Abstract

We present a general scheme to find variationally characterized critical points of a functional $I\colon H \to \mathbb{R}$ on a Hilbert space $H$ with hypothesis where the usual Nehari method is not directly applicable. These critical points arise as minima of $I$ over a suitable subset of the associated Nehari set and are obtained with the aid of fibering methods. Moreover, we derive a comparison result with mountain pass critical values. The abstract results will be applied to classes of logarithmic Choquard and nonlinear Schrödinger equations.

Citation

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Omar Cabrera Chavez. "Partial minimization over the Nehari set and applications to elliptic equations." Topol. Methods Nonlinear Anal. 63 (2) 559 - 593, 2024. https://doi.org/10.12775/TMNA.2023.031

Information

Published: 2024
First available in Project Euclid: 17 July 2024

Digital Object Identifier: 10.12775/TMNA.2023.031

Keywords: Elliptic partial differential equatio , Ground states , logarithmic Choquard equation , Nehari manifold , nonlinear Schrödinger equation

Rights: Copyright © 2024 Juliusz P. Schauder Centre for Nonlinear Studies

Vol.63 • No. 2 • 2024
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