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.

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Publication Title

Nonlinear Differ. Equ. Appl.

DOI

10.1007/s00030-023-00896-2

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