Partial minimization over the Nehari set and applications to elliptic equations
DOI:
https://doi.org/10.12775/TMNA.2023.031Keywords
Elliptic partial differential equatio, logarithmic Choquard equation, nonlinear Schrödinger equation, Nehari manifold, ground statesAbstract
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.References
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Copyright (c) 2024 Omar Cabrera Chavez
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