Singularly perturbed elliptic systems |
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Authors: | Claudianor O Alves Sérgio HM Soares |
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Institution: | 1. Departamento de Matemática e Estatística, Universidade Federal de Campina Grande, 58109-970-Campina Grande-PB, Brazil;2. Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação-ICMC, Universidade de São Paulo-USP, 13560-970, São Carlos-SP, Brazil |
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Abstract: | We study the existence and concentration behavior of positive solutions for a class of Hamiltonian systems (two coupled nonlinear stationary Schrödinger equations). Combining the Legendre–Fenchel transformation with mountain pass theorem, we prove the existence of a family of positive solutions concentrating at a point in the limit, where related functionals realize their minimum energy. In some cases, the location of the concentration point is given explicitly in terms of the potential functions of the stationary Schrödinger equations. |
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Keywords: | 35A15 35J50 58J37 |
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