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Localization phenomena in a degenerate logistic equation

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Arrieta, José M. and Pardo, Rosa and Rodríguez Bernal, Aníbal (2014) Localization phenomena in a degenerate logistic equation. Electronic Journal of Differential Equations, Conference 21, 21 . pp. 1-9. ISSN 1072-6691

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Abstract

We analyze the behavior of positive solutions of elliptic equations with a degenerate logistic nonlinearity and Dirichlet boundary conditions. Our results concern existence and strong localization in the spatial region in which the logistic nonlinearity cancels. This type of nonlinearity has applications in the nonlinear Schrodinger equation and the study of Bose–Einstein condensates. In this context, our analysis explains the fact that the ground state presents a strong localization in the spatial region in which the nonlinearity cancels.


Item Type:Article
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Variational and Topological Methods: Theory, Applications, Numerical Simulations, and Open Problems (2012)

Subjects:Sciences > Mathematics > Differential equations
ID Code:33235
Deposited On:24 Sep 2015 06:45
Last Modified:12 Dec 2018 15:06

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