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.
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Alves, C.O., Soares, S.H.M. Existence and concentration of positive solutions for a class of gradient systems. Nonlinear differ. equ. appl. 12, 437–457 (2006). https://doi.org/10.1007/s00030-005-0021-8
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DOI: https://doi.org/10.1007/s00030-005-0021-8