Geodesic
Existence of least energy solutions to coupled elliptic systems with critical nonlinearities
Electronic journal of differential equations, Tome 2008 (2008)
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.
Classification : 35B33, 35J50
Keywords: least energy solutions, Nehari manifold, critical exponent, coupled elliptic systems 
@article{EJDE_2008__2008__a62,
     author = {Wei,  Gongming and Wang,  Yanhua},
     title = {Existence of least energy solutions to coupled elliptic systems with critical nonlinearities},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1170.35323},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a62/}
}
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%A Wang,  Yanhua
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%J Electronic journal of differential equations
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Wei,  Gongming; Wang,  Yanhua. Existence of least energy solutions to coupled elliptic systems with critical nonlinearities. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a62/