Open Access
2007 On local compactness in quasilinear elliptic problems
Khalid Adriouch, Abdallah El Hamidi
Differential Integral Equations 20(1): 77-92 (2007). DOI: 10.57262/die/1356050281


One of the major difficulties in nonlinear elliptic problems involving critical nonlinearities is the compactness of Palais-Smale sequences. In their celebrated work [7], Brézis and Nirenberg introduced the notion of critical level for these sequences in the case of a critical perturbation of the Laplacian homogeneous eigenvalue problem. In this paper, we give a natural and general formula of the critical level for a large class of nonlinear elliptic critical problems. The sharpness of our formula is established by the construction of suitable Palais-Smale sequences which are not relatively compact.


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Khalid Adriouch. Abdallah El Hamidi. "On local compactness in quasilinear elliptic problems." Differential Integral Equations 20 (1) 77 - 92, 2007.


Published: 2007
First available in Project Euclid: 21 December 2012

zbMATH: 1212.35161
MathSciNet: MR2282827
Digital Object Identifier: 10.57262/die/1356050281

Primary: 35J60
Secondary: 35J25 , 35J70 , 47J30 , 58E05

Rights: Copyright © 2007 Khayyam Publishing, Inc.

Vol.20 • No. 1 • 2007
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