School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Multiple Critical Points of a Functional in Product Spaces with Applications to Elliptic Systems
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.
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
Comments
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