Abstract
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.
Citation
Khalid Adriouch. Abdallah El Hamidi. "On local compactness in quasilinear elliptic problems." Differential Integral Equations 20 (1) 77 - 92, 2007. https://doi.org/10.57262/die/1356050281
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