Multiple Critical Points of a Functional in Product Spaces with Applications to Elliptic Systems

Authors

Xiyou Cheng
Zhaosheng Feng, The University of Texas Rio Grande Valley
Lei Wei

Document Type

Article

Publication Date

2023

Abstract

In this paper, we deal with the existence and multiplicity of component-wise nontrivial critical points (i.e., whose components are both nonzero) for an abstract C1 -functional J defined in X×X with X being a reflexive Banach space. Applying the Nehari manifold method and the minimization method along with the geometric properties of the constructed functions, we investigate the existence and multiplicity of component-wise nontrivial critical points of J. As applications, we prove the existence and multiplicity of component-wise nontrivial solutions for the second-order and fourth-order elliptic systems. Our theoretical results improve and extend the relevant results in the existing literature.

Comments

Copyright © 2022, Mathematica Josephina, Inc.

Recommended Citation

Cheng, X., Feng, Z. & Wei, L. Multiple Critical Points of a Functional in Product Spaces with Applications to Elliptic Systems. J Geom Anal 33, 36 (2023). https://doi.org/10.1007/s12220-022-01149-x

Publication Title

J Geom Anal

DOI

10.1007/s12220-022-01149-x