Localization phenomena in a degenerate logistic equation

  1. José M. Arrieta 1
  2. Rosa Pardo 1
  3. Aníbal Rodríguez-Bernal 1
  1. 1 Universidad Complutense de Madrid
    info

    Universidad Complutense de Madrid

    Madrid, España

    ROR 02p0gd045

Revista:
Electronic Journal of Differential Equations

ISSN: 1550-6150 1072-6691

Año de publicación: 2014

Volumen: Conference 21

Páginas: 1-9

Tipo: Artículo

Otras publicaciones en: Electronic Journal of Differential Equations

Resumen

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.

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