A concentration-compactness lemma with applications to singular eigenvalue problems
A concentration-compactness lemma with applications to singular eigenvalue problems
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DOI：
10.1006/jfan.1999.3461
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发表时间：
1999-10
影响因子：
1.7
通讯作者：
D. Smets
中科院分区：
文献类型：
--
作者：
D. Smets
设R-N的Omega子集或等于R-N是任意开集。研究了非线性特征值问题-Delta(P)u=lambda V(X)u(p-2)u，u epsilon D-0(1，p)(Omega)，其中1<；p<；N和V是L的元素-loc(1)(Omega)可能具有强奇性和不定符号。关键成分是与依赖于V的极限问题有关的精确的浓度紧性引理。这项工作遵循、推广和简化了A.Tertikas(1998，J.Funct.肛门。154，42-66)处理Omega=R-N的正线性情形。(C)1999年学术出版社。
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.