A concentration-compactness lemma with applications to singular eigenvalue problems

Smets, D
(1999) Journal of Functional Analysis — Vol. 167, n° 2, p. 463-480 (1999)

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  • Smets, D
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Abstract
Let Omega subset of or equal to R-N be any open set. We study the nonlinear eigenvalue problem - Delta(p)u = lambda V(x) u(p-2) u, u epsilon D-0(1,p)(Omega) where 1 < p < N and V is an element of L-loc(1)(Omega) may have strong singularities and an indefinite sign. The key ingredient is a precised concentration-compactness lemma related to V-dependent limiting problems. This work follows, extends, and simplifies that of A. Tertikas (1998, J. Funct. Anal. 154, 42-66) dealing with the positive linear case for Omega = R-N. (C) 1999 Academic Press.
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Smets, D. (1999). A concentration-compactness lemma with applications to singular eigenvalue problems. Journal of Functional Analysis, 167(2), 463-480. https://doi.org/10.1006/jfan.1999.3461 (Original work published 1999)