Electron. J. Diff. Eqns., Vol. 2008(2008), No. 49, pp. 1-8.

Existence of least energy solutions to coupled elliptic systems with critical nonlinearities

Gong-Ming Wei, Yan-Hua Wang

In this paper we study the existence of nontrivial solutions of elliptic systems with critical nonlinearities and subcritical nonlinear coupling interactions, under Dirichlet or Neumann boundary conditions. These equations are motivated from solitary waves of nonlinear Schrodinger systems in physics. Using minimax theorem and by estimates on the least energy, we prove the existence of nonstandard least energy solutions, i.e. solutions with least energy and each component is nontrivial.

Submitted October 18, 2007. Published April 4, 2008.
Math Subject Classifications: 35B33, 35J50.
Key Words: Least energy solutions; Nehari manifold; critical exponent; coupled elliptic systems.

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Gong-Ming Wei
Tin Ka-Ping College of Science
University of Shanghai for Science and Technology
Shanghai, 200093, China
email: gmweixy@163.com
Yan-Hua Wang
Department of Applied Mathematics
Shanghai University of Finance and Economics
Shanghai, 200433, China
email: yhw@mail.shufe.edu.cn

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