Nondegeneracy of solutions for a class of cooperative systems on $ \mathbb{R}^n $
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<p style='text-indent:20px;'>We consider fully coupled cooperative systems on <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^n $\end{document}</tex-math></inline-formula> with coefficients that decay exponentially at infinity. Expanding some results obtained previously on bounded domain, we prove that the existence of a strictly positive supersolution ensures the first eigenvalue to exist and to be nonzero. This result is applied to show that the topological solutions for a Chern-Simons model, described by a semilinear system on <inline-formula><tex-math id="M3">\begin{document}$ \mathbb{R}^2 $\end{document}</tex-math></inline-formula> with exponential nonlinearity, are nondegenerate.</p>
2019 ◽
Vol 22
(5)
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pp. 1414-1436
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2021 ◽
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2015 ◽
Vol 17
(06)
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pp. 1450044
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Estimates for The First Eigenvalue of the Sturm–Liouville Problem with Potentials in Weighted Spaces
2019 ◽
Vol 244
(2)
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pp. 216-234
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