Electron. J. Diff. Equ., Vol. 2012 (2012), No. 39, pp. 1-11.

Singular elliptic systems involving concave terms and critical Caffarelli-Kohn-Nirenberg exponents

Mohammed E. O. El Mokhtar

In this article, we establish the existence of at least four solutions to a singular system with a concave term, a critical Caffarelli-Kohn-Nirenberg exponent, and sign-changing weight functions. Our main tools are the Nehari manifold and the mountain pass theorem.

Submitted July 21, 2011. Published March 14, 2012.
Math Subject Classifications: 35J66, 35J55, 35B40.
Key Words: Singular elliptic system; concave term; mountain pass theorem; critical Caffarelli-Kohn-Nirenberg exponent; Nehari manifold; sign-changing weight function.

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Mohammed El Mokhtar Ould El Mokhtar
University of Tlemcen
Dynamics Systems Laboratoire and Applications
BO 119, 13 000, Tlemcen, Algeria
email: med.mokhtar66@yahoo.fr

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