Multiplicity of solutions for a noncooperative elliptic system with critical Sobolev exponent

2008 ◽  
Vol 60 (3) ◽  
pp. 402-415 ◽  
Author(s):  
Fang Lin ◽  
Yongqing Li
Keyword(s):  
Elliptic System ◽  
Critical Sobolev Exponent ◽  
Multiplicity Of Solutions ◽  
Noncooperative Elliptic System ◽  
Sobolev Exponent

A Nonhomogeneous Fractional p-Kirchhoff Type Problem Involving Critical Exponent in ℝ N

2017 ◽  
Vol 17 (3) ◽  
Author(s):  
Mingqi Xiang ◽  
Binlin Zhang ◽  
Xia Zhang
Keyword(s):  
Critical Exponent ◽  
Critical Sobolev Exponent ◽  
Type Problem ◽  
Multiplicity Of Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Problem ◽  
Sobolev Exponent

AbstractThis paper concerns itself with the nonexistence and multiplicity of solutions for the following fractional Kirchhoff-type problem involving the critical Sobolev exponent:where

scholarly journals A note on the variational structure of an elliptic system involving critical Sobolev exponent

2003 ◽  
Vol 2003 (5) ◽  
pp. 227-241
Author(s):  
Mario Zuluaga
Keyword(s):  
Maximum Principle ◽  
Variational Methods ◽  
Elliptic System ◽  
Elliptic Systems ◽  
Critical Sobolev Exponent ◽  
Growth Conditions ◽  
Scalar Case ◽  
Biharmonic Equations ◽  
Variational Structure ◽  
Sobolev Exponent

We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by Fleckinger et al. (1995), we can find positive solutions. Also, we generalize the systems results obtained (for the scalar case) by Brézis and Nirenberg (1983). Also, we give applications to biharmonic equations.

Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential

2010 ◽  
Vol 62 (1) ◽  
pp. 19-33
Author(s):  
Mohammed Bouchekif ◽  
Yasmina Nas
Keyword(s):  
Variational Methods ◽  
Elliptic System ◽  
Bounded Domain ◽  
Elliptic Systems ◽  
Critical Sobolev Exponent ◽  
Existence Results ◽  
Hardy Potential ◽  
Semilinear Elliptic Systems ◽  
Semilinear Elliptic ◽  
Sobolev Exponent

AbstractIn this paper we consider an elliptic system with an inverse square potential and critical Sobolev exponent in a bounded domain of ℝN. By variational methods we study the existence results.

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