Existence and concentration of positive solutions for a class of gradient systems

Original Paper

DOI: 10.1007/s00030-005-0021-8

Cite this article as:
Alves, C.O. & Soares, S.H.M. Nonlinear differ. equ. appl. (2006) 12: 437. doi:10.1007/s00030-005-0021-8


Some gradient systems with two competing potential functions are considered. Bound states (solutions with finite energy) are proved to exist and to concentrate at a point in the limit. The proof relies on variational methods, where the existence and concentration of positive solutions are related to a suitable ground energy function.

Mathematics Subject Classification (2000).


Key words and phrases.

variational methodsgradient systemspositive solutionsconcentration

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidade Federal de Campina Grande - UFCGCampina GrandeBrazil
  2. 2.Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação -ICMCUniversidade de São Paulo - USPSão CarlosBrazil