Author(s) |
Wei, Lei
Du, Yihong
|
Publication Date |
2019
|
Abstract |
<p>In this paper, we study positive solutions of the elliptic equation
</p><p>
βΞπ’=ππ(π₯)πΌπ’βπ(π₯)ππ’πinΞ©,
</p><p>
where πΌ>2,π>βπΌ, π>1, π(π₯)=πππ π‘(π₯,πΞ©), and Ξ© is a bounded smooth domain in βπ(πβ©Ύ2). When πΌ=2, the term 1π(π₯)πΌ=1π(π₯)2 is often called a Hardy potential, and the equation in this case has been extensively investigated. Here we consider the case πΌ>2, which gives a stronger singularity than the Hardy potential near πΞ©. We show that when π<0, the equation has no positive solution, while when π>0, the equation has a unique positive solution, and it satisfies
</p><p>
limπ(π₯)β0π’(π₯)π(π₯)πΌ+ππβ1=π1πβ1.</p>
|
Citation |
Bulletin of the London Mathematical Society, 51(2), p. 251-266
|
ISSN |
1469-2120
0024-6093
|
Link | |
Publisher |
Wiley-Blackwell Publishing Ltd
|
Title |
Positive solutions of elliptic equations with a strong singular potential
|
Type of document |
Journal Article
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Entity Type |
Publication
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