Concentration-compactness at the mountain pass level in semilinear elliptic problems
نویسنده
چکیده
The concentration compactness framework for semilinear elliptic equations without compactness, set originally by P.-L.Lions for constrained minimization in the case of homogeneous nonlinearity, is extended here to the case of general nonlinearities in the standard mountain pass setting of Ambrosetti–Rabinowitz. In these setting, existence of solutions at the mountain pass level c is verified under a single assumption c < c∞, where c∞ is the mountain pass level for the asymptotic problem, which is completely analogous to the Lions’ case. Problems on RN and problems with critical nonlinearity are considered. Particular attention is given to nonhomogeneous critical nonlinearities that oscillate about the “critical stem” F (u) = |u|2 ∗ . 2000 Mathematics Subject Classification: 35J20, 35J60, 49J35
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