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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Article
On Nonhomogeneous Singular Elliptic Systems with Critical C-K-N Exponent
Author(s)
Mohammed El Mokhtar Ould El Mokhtar
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DOI:10.17265/2159-5291/2015.04.005
Affiliation(s)
Qassim University, College of Science, Kingdom of Saudi Arabia, Departement of Mathematics, BO 6644, Buraidah: 51452.
ABSTRACT
In this paper, we are
interested in the existence and multiplicity results of nontrivial solutions to
nonhomogeneous singular elliptic systems with critical C-K-N exponent 
. With the help of the Nehari manifold and under
sufficient conditions on the parameters λ1 and λ2, we prove some existence results.
KEYWORDS
Singular nonhomogeneous elliptic systems, Nehari manifold, critical C-K-N exponent
Cite this paper
References
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[2] M. Bouchekif, A. Matallah, On singular nonhomogeneous elliptic equations involving critical Caffarelli-Kohn-Nirenberg exponent, Ric. Mat., 58 (2009) 207-218.
[3] K. J. Brown, Y. Zhang, The Nehari manifold for a semilinear elliptic equation with a sign changing weight function, J. Differential Equations, 2 (2003) 481--499.
[4] L. Caffarelli, R. Kohn, L. Nirenberg: First order interpolation inequality with weights, Compos. Math., 53 (1984) 259-275.
[5] K.S. Chou, C.W. Chu, On the best constant for a weighted Sobolev-Hardy Inequality, J. Lond. Math. Soc., 2 (1993) 137-151.
[6] D. G. de Figueiredo, Semilinear elliptic systems, Lecture Notes at the Second School on Nonlinear functional analysis and application to differential equations, held at ICTP of Trieste, April 21-May 9, (1997).
[7] D. Kang, S. Peng, Positive solutions for singular elliptic problems, Appl. Math. Lett., 17 (2004) 411-416.
[8] Z. Liu, P. Han, Existence of solutions for singular elliptic systems with critical exponents, Nonlinear Anal., 69 (2008) 2968-2983.
[9] G. Tarantello, Multiplicity results for an inhomogeneous Neumann problem critical exponent, Manuscripta Math., 81 (1993) 57-78.
[10] Z. Wang, H. Zhou, Solutions for a nonhomogeneous elliptic problem involving critical Sobolev-Hardy exponent in
, Acta Math. Sin. (Engl. Ser.), 26 (2006) 525-536.