Original Paper

Nonlinear Differential Equations and Applications NoDEA

, Volume 12, Issue 4, pp 437-457

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

  • Claudianor O. AlvesAffiliated withDepartamento de Matemática, Universidade Federal de Campina Grande - UFCG Email author 
  • , Sérgio H. M. SoaresAffiliated withDepartamento de Matemática, Instituto de Ciências Matemáticas e de Computação -ICMC, Universidade de São Paulo - USP

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Abstract.

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).

35A15 35J50 58J37

Key words and phrases.

variational methods gradient systems positive solutions concentration