Variational and Topological Methods: Theory, Applications, 
Numerical Simulations, and Open Problems.
Electron. J. Diff. Eqns., Conference 21 (2014), pp. 1-9

Title: Localization phenomena in a degenerate logistic equation

Authors: Jose M. Arrieta (Univ. Complutense de Madrid, Spain)
         Rosa Pardo      (Univ. Complutense de Madrid, Spain)
         Anibal Rodriguez-Bernal (Univ. Complutense de Madrid, Spain)
 
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.