Jose M. Arrieta, Rosa Pardo, Anibal Rodriguez-Bernal
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.
Published February 10, 2014.
Math Subject Classifications: 35B32, 35B35, 35B65, 35B40, 35B41, 35B44, 35J25.
Key Words: Logistic equation; positive solution; bifurcation; localization;
blow-up.
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José M. Arrieta Departamento de Matemática Aplicada Universidad Complutense de Madrid 28040 - Madrid, Spain email: arrieta@mat.ucm.es |
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Rosa Pardo Departamento de Matemática Aplicada Universidad Complutense de Madrid 28040 - Madrid, Spain email: rpardo@mat.ucm.es |
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Anibal Rodríguez-Bernal Departamento de Matemática Aplicada Universidad Complutense de Madrid 28040 - Madrid, Spain. Instituto de Ciencias Matemáticas CSIC-UAM-UC3M-UCM, 28049--Madrid, Spain email: arober@mat.ucm.es |
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