Author(s) |
Cao, Daomin
Yan, Shusen
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Publication Date |
2010
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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.
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Citation |
Calculus of Variations and Partial Differential Equations, 38(3-4), p. 471-501
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ISSN |
1432-0835
0944-2669
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Link | |
Publisher |
Springer
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Title |
Infinitely many solutions for an elliptic problem involving critical Sobolev growth and Hardy potential
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Type of document |
Journal Article
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Entity Type |
Publication
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