Qualitative properties of multi-bubble solutions for nonlinear elliptic equations involving critical exponents
- Authors
- Choi, Woocheol; Kim, Seunghyeok; Lee, Ki-Ahm
- Issue Date
- Aug-2016
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Asymptotic behavior of solutions; Critical exponents; Linearized problem; Multi-bubble solutions
- Citation
- ADVANCES IN MATHEMATICS, v.298, pp.484 - 533
- Indexed
- SCIE
SCOPUS
- Journal Title
- ADVANCES IN MATHEMATICS
- Volume
- 298
- Start Page
- 484
- End Page
- 533
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/154093
- DOI
- 10.1016/j.aim.2016.03.043
- ISSN
- 0001-8708
- Abstract
- The objective of this paper is to obtain qualitative characteristics of multi-bubble solutions to the Lane-Emden-Fowler equations with slightly subcritical exponents given any dimension n >= 3. By examining the linearized problem at each m-bubble solution, we provide a number of estimates on the first (n + 2)m-eigenvalues and their corresponding eigenfunctions. Specifically, we present a new and unified proof of the classical theorems due to Bahri-Li-Rey (1995) [2] and Rey (1999) [24] which state that if n >= 4 or n = 3, respectively, then the Morse index of a multi-bubble solution is governed by a certain symmetric matrix whose component consists of a combination of Green's function, the Robin function, and their first and second derivatives.
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