School of Mathematical and Statistical Sciences Faculty Publications and Presentations
Existence and non-existence results for cooperative elliptic systems without variational structure
Document Type
Article
Publication Date
2024
Abstract
We consider general cooperative elliptic systems possibly without variational structure and with differential operator resembling that from an Euler–Lagrange equation for a sharp Hardy–Sobolev inequality. Under suitable growth conditions on the source nonlinearities and geometric assumptions on the domain, we derive various existence and non-existence results and Liouville theorems. The results are obtained by incorporating and adapting various techniques, including variants of the method of moving planes enhanced by Kelvin and Emden–Fowler type transformations, as well as degree theoretic shooting methods.
Recommended Citation
Villavert, J. Existence and non-existence results for cooperative elliptic systems without variational structure. Nonlinear Differ. Equ. Appl. 31, 12 (2024). https://doi.org/10.1007/s00030-023-00896-2
Publication Title
Nonlinear Differ. Equ. Appl.
DOI
10.1007/s00030-023-00896-2
Comments
Reprints and permissions
https://rdcu.be/dyJYh