On systems of elliptic equations involving subcritical or critical Sobolev exponents

By Claudianor Oliveira Alves, Daniel C. Morais Filho, M. Souto. 2000

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The Nehari manifold for fractional systems involving critical nonlinearities (2015, background): “1) for the Laplacian operator have been studied extensively in recent years, see [1, 13, 19, 20, 30, 31] and the references therein.”
The Nehari manifold for a semilinear elliptic system involving sign-changing weight functions (2008, methodology): “For more similar problems, we refer the reader to Ahammou [1], Alves–de Morais Filho–Souto [5], Bozhkov–Mitidieri [6], Clément–de Figueiredo–Mitidieri [7], de Figueiredo–Felmer [8], EL Hamidi [11], Squassina [13] and Vélin [15], etc.”
On the singular elliptic systems involving multiple critical Sobolev exponents (2011, background): “The proof is omitted for simplicity (see also [5]).”