Open AccessNondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $
Author(s) -
Marcello Lucia,
Guido Sweers
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021152
Subject(s) - bounded function , infinity , mathematics , domain (mathematical analysis) , class (philosophy) , eigenvalues and eigenvectors , exponential function , exponential growth , combinatorics , pure mathematics , physics , mathematical analysis , computer science , quantum mechanics , artificial intelligence
We consider fully coupled cooperative systems on \begin{document}$ \mathbb{R}^n $\end{document} with coefficients that decay exponentially at infinity. Expanding some results obtained previously on bounded domain, we prove that the existence of a strictly positive supersolution ensures the first eigenvalue to exist and to be nonzero. This result is applied to show that the topological solutions for a Chern-Simons model, described by a semilinear system on \begin{document}$ \mathbb{R}^2 $\end{document} with exponential nonlinearity, are nondegenerate.