Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential

Author(s)
Cao, Daomin
Yan, Shusen
Publication Date
2010
Abstract
The aim of this paper is to prove that (1.1) has infinitely many solutions if N ≥ 7 and 0 ≤ μ < (N-2)²/4 − 4. As in [13] one of the major difficulty to prove the existence of infinitely many solutions for (1.1) by using the variational methods is that I (u) does not satisfy the Palais–Smale condition for large energy level, since 2* is the critical exponent for the Sobolev embedding from H¹(Ω) to Lq(Ω). Another difficulty is that, unlike in [13], every nontrivial solution of (1.1) is singular at x = 0 if μ ≠ 0 (see [8,9]). So, different techniques are needed to deal with the case μ > 0.
Citation
Calculus of Variations and Partial Differential Equations, 38(3-4), p. 471-501
ISSN
1432-0835
0944-2669
Link
Publisher
Springer
Title
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential
Type of document
Journal Article
Entity Type
Publication

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